1
The outward bulging surface of a spoon is like which mirror?
💡 Hint:
The image stays erect and small.
Explanation:
The outward surface is like a convex mirror. The inward surface is like a concave mirror.
Class 10 · Science · Chapter 9 · बिहार बोर्ड (BSEB)CBSE · NCERT 2026-27
Light — Reflection and Refraction
Light — Reflection and Refraction
How to use this page:
1. Read — Activities 9.1 to 9.13 · spoon, mirrors, coin, slab and lenses, diagram, worked example, board tip
2. Check — each lesson has its own questions; the number follows the lesson
3. Mastery ★ — all of that lesson correct. Redo the wrong ones
4. Look at the sign-convention figure: the object is on the left, and distances are measured from the pole or the optical centre.
In NCERT 2026-27 this is chapter 9. In the older 16-chapter Bihar book the same text is chapter 10. Progress stays in this browser.
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- 1 Two faces of a spoon — Activity 9.1
- 2 Focal length of a concave mirror — Activity 9.2
- 3 Centre of curvature and the candle — Activity 9.3
- 4 Ray diagrams and the mirror formula — Activity 9.4
- 5 Convex mirror — Activity 9.5
- 6 Plane mirror — Activity 9.6
- 7 The coin and apparent depth — Activities 9.7 and 9.8
- 8 Glass slab and Snell — Activities 9.9 and 9.10
- 9 Convex lens, image positions and the lens formula — Activities 9.11 and 9.12
- 10 Concave lens — Activity 9.13
- Chapter winner — every lesson at mastery ★
🎬 Shorts
This chapter has no Short on the channel yet, so ten empty cards are not shown. The notes, diagrams and checks are complete.
📄 PDF download — notes + answer key
Two faces of a spoon — Activity 9.1
चम्मच के दो पृष्ठ — क्रियाकलाप 9.1 · NCERT 9.1 · Activity 9.1
Light seems to travel in a straight lineNotes
An object is invisible in a dark room. When light falls on it, the object sends that light back, and the light that enters the eye lets us see the object. Light passes through a transparent medium.
In this chapter we treat a ray as a straight line. The two laws of reflection hold for every polished surface, including a spherical one. Angle of incidence = angle of reflection. The incident ray, the normal and the reflected ray lie in one plane.
The image in a plane mirror is always virtual and erect, the same size as the object, and as far behind as the object is in front. It is also laterally inverted.
Activity 9.1 — a shining spoonActivity
Take a large shining spoon. First look at your face in the surface that caves inward. Held close, the image looks erect and enlarged. Move the spoon slowly away. After a certain distance the face begins to look inverted and smaller.
Now turn the spoon over and look in the surface that bulges outward. The image stays erect and small. The inner surface behaves like a concave mirror and the outer one like a convex mirror. A spherical mirror is part of the surface of a sphere. In the diagram the back of the mirror is shaded — that side does not shine.
Worked exampleExample
Question: Which surface of the spoon behaves like a shaving mirror, and why?
Answer: The surface that caves inward. Brought close, it gives an erect, enlarged image, as a concave mirror does when the face is between the pole and the focus.
10-second revision
- Inward surface = concave; outward bulge = convex
- Close concave: erect and large; farther away it can become inverted and small
- A convex surface always gives an erect, diminished image
Board tip · BSEBBoard tip
In an objective item name the spoon’s surface — only “shining” is incomplete.
Board tip · CBSEBoard tip
If CBSE asks the laws, write both: angles equal, and the three rays in one plane. One law leaves half the mark.
Check your understandingall correct = mastery ★
2
The laws of reflection apply only to a plane mirror.
Explanation:
False — the same laws apply to spherical surfaces too.
3
The angle of incidence is ______ the angle of reflection.
💡 Hint:
The first law.
Explanation:
The angle of incidence equals the angle of reflection.
4
In Activity 9.1, how does the image in the inner surface change as the spoon is moved away?
Model answer (board format)
Held close, the face looks erect and enlarged. After the spoon is moved away, beyond one position the image becomes inverted and smaller. The outer surface does not invert like that.
Check your answer:
Focal length of a concave mirror — Activity 9.2
अवतल दर्पण की फोकस दूरी — क्रियाकलाप 9.2 · NCERT 9.2 · Activity 9.2 · caution
Do not look toward the SunCaution
Caution: Do not look at the Sun directly, and do not look into a mirror that is reflecting sunlight. The eyes can be damaged. Watch only the bright spot on the paper.
Activity 9.2 — a sharp spot on paperActivity
Hold a concave mirror and turn its shining surface toward the Sun. Direct the reflected light onto a sheet of paper held near the mirror. Move the paper back and forth until a sharp bright spot appears.
Keep that position for a few minutes. The paper first smokes and may then catch fire. The sun’s rays are gathered at that point. That point is the focus of the mirror, and it is a tiny real image of the Sun. The distance from the mirror to this spot is the approximate focal length.
Pole, focus and R = 2fNotes
The middle point of the shining surface is the pole P. It lies on the mirror. The centre of the sphere of which this surface is a part is the centre of curvature C. C is not on the mirror. For a concave mirror C is in front; for a convex mirror it is behind. PC is the radius of curvature R.
The line through P and C is the principal axis. It is normal to the mirror at the pole. Rays parallel to the axis, after reflection from a concave mirror, pass through one point on the axis. That is the principal focus F. From a convex mirror the reflected rays appear to come from such a point. PF = f.
For a mirror of small aperture, R = 2f. The focus lies midway between the pole and the centre of curvature. The aperture is the diameter of the shining surface.
Worked exampleExample
Question: A spherical mirror has a radius of curvature of 20 cm. What is its focal length?
Formula: f = R / 2
Substitute: f = 20 cm / 2 = 10 cm
The signs come later. If the mirror is concave, the focus is in front and f = −10 cm. If it is convex, f = +10 cm.
10-second revision
- Do not look at the Sun or at its image in the mirror
- The paper burns because the rays gather at the focus
- R = 2f; the focus is midway between P and C
Board tip · BSEBBoard tip
The caution earns its own mark. Write “the eyes can be damaged” in the answer.
Board tip · CBSEBoard tip
CBSE expects 10 cm when R = 20 cm. Add a sign only when the question says concave or convex.
Check your understandingall correct = mastery ★
1
Why can the paper catch fire in Activity 9.2?
💡 Hint:
The sharp bright spot.
Explanation:
The rays gather at one point. That is the focus, and the heat burns the paper.
2
In this activity it is safe to look at the Sun’s image by putting the eye to the mirror.
Explanation:
False — the caution is not to look at the Sun directly or by way of the mirror.
3
If the radius of curvature is 32 cm, the size of the focal length is ______ cm.
💡 Hint:
f = R/2.
Explanation:
f = 32 cm / 2 = 16 cm. For a convex mirror the signed value is f = +16 cm.
4
For a spherical mirror of small aperture, where is the focus?
💡 Hint:
R = 2f.
Explanation:
F lies midway between the pole and the centre of curvature.
5
Why does a concave mirror burn paper with sunlight? Also write the caution.
Model answer (board format)
Parallel rays meet at the focus after reflection. Heat collects there and burns the paper. Do not look at the Sun directly or in the mirror; the eyes can be damaged.
Check your answer:
Centre of curvature and the candle — Activity 9.3
वक्रता केन्द्र और मोमबत्ती — क्रियाकलाप 9.3 · NCERT 9.2.1 · Activity 9.3 · Table 9.1
P, F and C on one lineNotes
The distance from Activity 9.2 is the approximate f. For a small aperture, F is midway between the pole and the centre of curvature, so C lies at 2f. The image in a concave mirror depends on where the object is — sometimes real, sometimes virtual; sometimes large, sometimes small.
Activity 9.3 — place the candle in six positionsActivity
Find the approximate f of a concave mirror. Draw a line on the table and place the pole on it. Then draw two more parallel lines separated by f. These stand for P, F and C.
First keep a burning candle far beyond C. Move a screen until a sharp image of the flame appears. Then place the candle (a) just beyond C, (b) at C, (c) between F and C, (d) at F, and (e) between P and F.
In one position the screen catches no image. That place is between P and F. Then look for the image in the mirror itself — virtual, erect and enlarged. At F the rays leave parallel, so no image is formed at a finite distance.
| Object | Image | Size | Nature |
|---|---|---|---|
| Infinity | At F | Point-sized | Real, inverted |
| Beyond C | Between F and C | Diminished | Real, inverted |
| At C | At C | Same size | Real, inverted |
| Between C and F | Beyond C | Enlarged | Real, inverted |
| At F | At infinity | Not formed | — |
| Between P and F | Behind the mirror | Enlarged | Virtual, erect |
Worked exampleExample
Question: A shaving mirror shows the face enlarged and erect. Where is the face?
Answer: Between the pole and the focus. In the table only this one place gives a virtual, erect and enlarged image. A dentist’s mirror works in the same place.
10-second revision
- Lines spaced by f stand for P, F and C
- The image that misses the screen belongs to an object between P and F
- An object at C gives an image at C, same size, inverted
Board tip · BSEBBoard tip
The last row of the table is asked most often. Among the six rows only that one is virtual.
Board tip · CBSEBoard tip
CBSE asks what real means. A real image can be taken on a screen and is inverted. A virtual image is seen only in the mirror.
Check your understandingall correct = mastery ★
1
If the object is between P and F of a concave mirror, the image is —
💡 Hint:
It does not appear on a screen.
Explanation:
This is the one position that gives a virtual, erect and enlarged image.
2
If the object is at the centre of curvature, the image is also at the centre of curvature and of the same size.
Explanation:
True — and it is real and inverted.
3
A concave mirror is used in a torch and a car headlight because —
💡 Hint:
Parallel rays are tied to the focus. The reverse path works too.
Explanation:
A ray starting from the focus becomes parallel to the principal axis after reflection. That gives a powerful beam.
4
If the object is at F, the image in a concave mirror is formed at ______.
💡 Hint:
The rays leave parallel.
Explanation:
The image is formed at infinity, not on a nearby screen.
5
In Activity 9.3, why does the screen stay blank in one position?
Model answer (board format)
When the candle is between P and F, the reflected rays do not meet in front. They appear to meet behind the mirror. The image is virtual and has to be seen in the mirror. The screen cannot catch it.
Check your answer:
Ray diagrams and the mirror formula — Activity 9.4
किरण आरेख और दर्पण सूत्र — क्रियाकलाप 9.4 · NCERT 9.2.2–9.2.4 · Activity 9.4 · sign convention
Activity 9.4 — a diagram for every row of the tableActivity
Draw a neat ray diagram for every object position in Table 9.1. To locate the image, take any two of these rays.
- A ray parallel to the axis passes through the focus of a concave mirror after reflection. From a convex mirror it appears to come from the focus.
- A ray through the focus comes out parallel to the axis after reflection.
- A ray through the centre of curvature returns on itself, because it meets the mirror along the normal.
- A ray toward the pole at a slant returns with i = r.
Compare your diagram with the book’s diagram and write the nature, place and size.
The New Cartesian sign convention and the formulaNotes
Take the pole as the origin. The object is always placed on the left, so that light comes from the left. Measure distances from the pole. The left side (the direction of the incident light) is negative, and the right side is positive. Above the axis is positive, below is negative.
So u is always negative. f is negative for a concave mirror and positive for a convex mirror. A real image in front of the mirror gives a negative v. A virtual image behind gives a positive v.
| Relation | Form | What to remember |
|---|---|---|
| Mirror formula | 1/v + 1/u = 1/f | Every spherical mirror, every position |
| Magnification | m = −v/u | A minus sign = real and inverted |
| From heights | m = h′/h | Take the object height as positive |
Worked example — one numerical, unit cmExample
Question: An object 4.0 cm high is 25 cm from a concave mirror. The focal length is 15 cm. Where should the screen be placed? What are the size and nature of the image?
Given: h = +4.0 cm, u = −25 cm, f = −15 cm. The mirror is concave, so f is negative. The object is on the left, so u is negative.
Formula: 1/v + 1/u = 1/f
Substitute: 1/v = 1/f − 1/u = 1/(−15) − 1/(−25) = −1/15 + 1/25
= −5/75 + 3/75 = −2/75
v = −37.5 cm
Magnification: m = −v/u = −(−37.5 cm)/(−25 cm) = −1.5
h′ = m × h = (−1.5) × (+4.0 cm) = −6.0 cm
Place the screen 37.5 cm in front of the mirror. The image is real, inverted and enlarged.
10-second revision
- Any two easy rays locate the image
- u is always negative; concave f is negative; formula 1/v + 1/u = 1/f
- m = −v/u; in the example above v = −37.5 cm and h′ = −6.0 cm
Board tip · BSEBBoard tip
Three lines are compulsory in a numerical: the formula, the substitution steps, and the answer with the unit cm.
Board tip · CBSEBoard tip
CBSE asks the reason for the sign. “Negative because it is concave” is only half. Write: the focus is in front of the mirror, and a distance in front is negative.
Check your understandingall correct = mastery ★
1
A ray parallel to the axis, after reflection from a concave mirror —
💡 Hint:
This is the definition of the focus.
Explanation:
A parallel ray passes through the focus of a concave mirror.
2
For a spherical mirror the object distance u is taken as positive.
Explanation:
False — the object is on the left, so u is negative.
3
The magnification of a mirror is m = ______.
💡 Hint:
The height form h′/h is also used.
Explanation:
m = −v/u. A negative sign means a real, inverted image.
4
In the worked example above, where is the screen?
💡 Hint:
v is negative.
Explanation:
v = −37.5 cm means 37.5 cm in front of the mirror. The image is real.
5
Assertion (A): The focal length of a concave mirror is written as negative.
Reason (R): In the sign convention a distance in front of the mirror is negative, and the focus is in front.
Explanation:
Both are true and R explains A.
6
Why does a ray through the centre of curvature return along the same path?
Model answer (board format)
That ray meets the mirror along the normal. The angle of incidence is zero, so the angle of reflection is also zero and the ray goes back along the same path.
Check your answer:
Convex mirror — Activity 9.5
उत्तल दर्पण — क्रियाकलाप 9.5 · NCERT Table 9.2 · Activity 9.5
Activity 9.5 — a pencil and a convex mirrorActivity
Hold a convex mirror in one hand and an upright pencil in the other. The image in the mirror is erect and diminished. Move the pencil slowly away. The image becomes still smaller.
As the object goes farther, the image moves away from the pole toward the focus. An object at infinity gives an image at the focus, point-sized, behind the mirror, virtual and erect.
| Object | Image | Size | Nature |
|---|---|---|---|
| Infinity | At F, behind | Point-sized | Virtual, erect |
| Between infinity and P | Between P and F, behind | Diminished | Virtual, erect |
The rear-view mirrorNotes
A convex mirror is fitted at the side of a vehicle. The image stays erect, even though it is small. The outward curve shows a wide field. The driver sees a large stretch behind at one time. A solar furnace or a headlight is not this job — those belong to a concave mirror.
Worked exampleExample
Question: A pencil is moving away from the mirror. Does the image in a convex mirror move toward the focus or toward the pole?
Answer: Toward the focus. The image of a nearby object is close to the pole. As the object moves toward infinity, the image moves toward F, but it does not cross F.
10-second revision
- A convex mirror always gives a virtual, erect and diminished image
- As the object moves away, the image comes closer to the focus
- The rear-view mirror is chosen because the field is wide and the image is erect
Board tip · BSEBBoard tip
“Always inverted” is the wrong option for a convex mirror. Inverted belongs to most positions of a concave mirror.
Board tip · CBSEBoard tip
CBSE asks for two reasons: an erect image and a wide field. One reason stays incomplete.
Check your understandingall correct = mastery ★
1
The image of a pencil in a convex mirror is —
💡 Hint:
Activity 9.5.
Explanation:
The image is erect and diminished, behind the mirror.
2
A convex mirror is fitted in a vehicle headlight to make a parallel beam.
Explanation:
False — a headlight uses a concave mirror. A convex mirror is for looking behind.
3
If the object comes from infinity toward the pole, the image in a convex mirror —
💡 Hint:
A distant object has its image near F.
Explanation:
At infinity the image is at F. As the object comes closer, the image leaves F and moves toward P.
4
Why is a convex mirror used as a rear-view mirror? Write two reasons.
Model answer (board format)
The image is always erect and diminished, so the object behind stays recognisable. The mirror bulges outward, so the field of view is wider than that of a plane mirror.
Check your answer:
Plane mirror — Activity 9.6
समतल दर्पण — क्रियाकलाप 9.6 · NCERT Activity 9.6 · plane mirror
Activity 9.6 — a distant tree in three mirrorsActivity
Look at the image of a distant tree in a plane mirror. Can you see the full length? Try plane mirrors of different sizes. A small mirror does not hold the whole tall tree at once.
Look at the same tree in a concave mirror. A full-length erect image is not easy there either. Now take a convex mirror. A small convex mirror shows the whole tree, because the field is wide and the image is formed small. Such a mirror on a wall of Agra Fort shows the full image of the Taj.
Four properties of a plane mirrorNotes
The image is virtual and erect. The size equals the object, so the magnification is m = +1. The plus sign says the image is erect. The image is as far behind as the object is in front. It is laterally inverted — right appears left.
However far you stand, the image in a plane mirror stays erect. A convex mirror does the same. A concave mirror gives an erect image only between P and F. So a mirror that stays erect at any distance is plane or convex.
Worked exampleExample
Question: The magnification of a plane mirror is +1. What does that mean?
Answer: The image is the same size as the object. The plus sign means an erect image, not an inverted one. The distances are equal too: if the object is 30 cm in front, the image is 30 cm behind.
10-second revision
- Plane: virtual, erect, same size, same distance, laterally inverted
- m = +1
- A whole large view fits in a small convex mirror, not in a small plane mirror
Board tip · BSEBBoard tip
Write both parts of m = +1 — same size and erect. Only “large” is wrong.
Board tip · CBSEBoard tip
Between the CBSE options “plane only” and “plane or convex”, the second is correct when the distance can be anything.
Check your understandingall correct = mastery ★
1
The magnification of a plane mirror is —
💡 Hint:
Same size and erect.
Explanation:
m = +1. The size is equal and the plus sign means an erect image.
2
A small plane mirror easily shows the full length of a distant tall tree.
Explanation:
False — in Activity 9.6 the full length is seen in a small convex mirror.
3
However far you stand, the image stays erect. The mirror can be —
💡 Hint:
A concave mirror is not erect in every position.
Explanation:
Both a plane mirror and a convex mirror give an erect image at every distance.
4
The right hand appearing as the left in a plane mirror is called ______.
💡 Hint:
The size does not change; left and right do.
Explanation:
This is called lateral inversion.
5
In Activity 9.6, why does a convex mirror show the whole tree?
Model answer (board format)
A convex mirror bulges outward, so the field of view is wide and the image is formed small. Even a small mirror holds the whole erect image of a tall tree. A plane mirror’s field is not that wide.
Check your answer:
The coin and apparent depth — Activities 9.7 and 9.8
सिक्का और आभासी गहराई — क्रियाकलाप 9.7, 9.8 · NCERT 9.3 · Activities 9.7 and 9.8
An oblique ray bendsNotes
Light travels straight in one medium. If it enters another transparent medium at a slant, the direction changes. That is refraction. The reason is that the speed of light is different in the two media.
The bottom of a pond looks raised. Letters under a glass slab look raised. A pencil half dipped in a glass looks bent at the surface. A lemon in water looks larger from the side. If kerosene replaces water, the bend is not the same — the effect depends on the pair of media.
Activity 9.7 — a coin in a bucketActivity
Place a coin at the bottom of a bucket filled with water. Keep the eye to one side above the water and try to pick the coin in one go. The hand usually comes up empty.
The coin is not seen at its real place. Because of refraction it looks raised a little. The hand goes to that apparent place. Repeat it, and let friends try — the experience stays the same.
Activity 9.8 — the coin that vanishes in a bowlActivity
Put a coin in a large shallow bowl. Step back slowly. Stop where the coin has just disappeared. Ask a friend to pour water gently into the bowl without moving the coin.
From the same place the coin becomes visible again. On adding water the coin appears raised, so a ray now reaches the eye. This is not magic; it is refraction.
Worked exampleExample
Question: A coin has disappeared in an empty bowl. The moment water is poured, the same coin is seen again. Did the coin really rise?
Answer: The coin did not rise. A ray from the water bent and reached the eye, so the coin appeared above its place. The real depth is greater and the apparent depth is less.
10-second revision
- Refraction = an oblique ray bending in the second medium
- The coin in the bucket looks raised, so the hand misses
- Water in the bowl shows the coin again by raising it apparently
Board tip · BSEBBoard tip
Write in the answer that the coin did not move. The ray did.
Board tip · CBSEBoard tip
In CBSE do not call apparent depth reflection. Here the bend comes from a change of medium, not from a mirror.
Check your understandingall correct = mastery ★
1
Why is the coin in a bucket of water not picked up in one try?
💡 Hint:
Activity 9.7.
Explanation:
The apparent position is above the real one, so the finger goes to the wrong place.
2
When water is poured into the bowl, the coin leaves its place and floats up.
Explanation:
False — the coin does not move. Refraction makes it look raised.
3
The bending of an oblique ray in a second medium is called ______.
💡 Hint:
Reflection belongs to a mirror.
Explanation:
This bending is called refraction.
4
In Activity 9.8, why does the person standing back see the coin again?
Model answer (board format)
After water is poured, a ray from the coin bends at the surface and reaches the eye. The coin appears raised, although it stays on the bottom of the bowl.
Check your answer:
Glass slab and Snell — Activities 9.9 and 9.10
काँच की सिल्ली और स्नेल — क्रियाकलाप 9.9, 9.10 · NCERT 9.3.1–9.3.2 · Activities 9.9, 9.10
Activity 9.9 — an ink line and a slabActivity
Draw a thick straight ink line on white paper. Place a glass slab so that one edge makes an angle with the line. Look from the side. The line under the slab looks bent at the edges.
Now place the slab normal to the line. The part underneath does not look bent at the edges. From above, that part of the line looks raised. At normal incidence the ray does not bend; at oblique incidence it does.
Activity 9.10 — four pinsActivity
Fix paper on a drawing board. Place a rectangular slab in the middle and draw its outline ABCD. Fix two pins E and F so that EF meets the edge AB at a slant. Looking from the opposite edge, fix two pins G and H so that all four appear in one line.
Remove the slab and the pins. Produce EF to AB, meeting at O. Produce HG to CD, meeting at O′. Join O and O′. The emergent ray is parallel to the incident ray, but shifted sideways. From air into glass (rarer into denser) the ray bends towards the normal. From glass into air it bends away from the normal. The bending at the two faces is equal and opposite.
Snell and refractive indexNotes
There are two laws of refraction. The incident ray, the refracted ray and the normal lie in one plane. For a given colour and a given pair, sin i / sin r stays constant. That is Snell’s law. The constant is the refractive index of the second medium with respect to the first.
n = sin i / sin r. The absolute refractive index is n = c / v, where c is the speed in vacuum and v the speed in the medium. c = 3 × 108 m/s. For water n is about 1.33, for crown glass 1.52, for diamond 2.42. The medium with the larger n is optically denser. This is not mass density — kerosene is optically denser than water, yet lighter in mass. Light travels faster in the rarer medium.
| Medium | n |
|---|---|
| Air | 1.0003 |
| Ice | 1.31 |
| Water | 1.33 |
| Kerosene | 1.44 |
| Crown glass | 1.52 |
| Diamond | 2.42 |
Worked exampleExample
Question: Light goes from air into glass. The refractive index of glass is 1.50. The speed in vacuum is 3 × 108 m/s. What is the speed in glass?
Formula: n = c / v, so v = c / n
Substitute: v = (3 × 108 m/s) / 1.50 = 2 × 108 m/s
Glass is optically denser, so the speed falls and an oblique ray bends towards the normal.
10-second revision
- In a slab the emergent ray is parallel, but shifted sideways
- Rarer to denser: towards the normal; denser to rarer: away
- n = sin i / sin r and n = c / v
Board tip · BSEBBoard tip
Lateral shift and bending are different words. The ray shifts even while it stays parallel.
Board tip · CBSEBoard tip
In CBSE, among water, kerosene and turpentine the fastest speed is in water, because n is the smallest. The whole table need not be memorised.
Check your understandingall correct = mastery ★
1
An oblique ray from air into glass bends —
💡 Hint:
Rarer to denser.
Explanation:
Glass is denser, the speed falls and the ray bends towards the normal.
2
The emergent ray from a rectangular slab is parallel to the incident ray.
Explanation:
True — the bending at the two faces is equal and opposite. The ray shifts sideways.
3
In Snell’s law, sin i / sin r is called the ______.
💡 Hint:
It is constant for the pair.
Explanation:
This is the refractive index. n = c/v says the same idea through speed.
4
Among water, kerosene and turpentine, light travels fastest in —
💡 Hint:
The smallest n. Water 1.33, kerosene 1.44, turpentine 1.47.
Explanation:
Water has the smallest refractive index, so the speed is the greatest.
5
The refractive index of diamond is 2.42. This means —
💡 Hint:
n = c/v, so v = c/n.
Explanation:
Light is slower in diamond. The speed in air is 2.42 times the speed in diamond.
6
In Activity 9.10, why does the emergent ray stay parallel to the incident ray?
Model answer (board format)
The two faces of the slab are parallel. At the first face, from air into glass, the ray bends towards the normal. At the second face, from glass into air, it bends by the same amount, the opposite way, away from the normal. So the emergent ray stays parallel to the incident ray and shifts a little sideways.
Check your answer:
Convex lens, image positions and the lens formula — Activities 9.11 and 9.12
उत्तल लेंस, प्रतिबिंब और लेंस सूत्र — क्रियाकलाप 9.11, 9.12 · NCERT 9.3.3–9.3.8 · Activities 9.11, 9.12
Do not look at the Sun through a lensCaution
Caution: During this activity or otherwise, do not look at the Sun directly or through a lens. The eyes can be damaged. Watch only the spot on the paper.
The lens and its formulaNotes
A lens is a transparent material bound by at least one spherical surface. A convex lens is thicker in the middle and gathers rays. A concave lens is thicker at the edge and spreads rays. The line through the two centres of curvature is the principal axis. The middle point is the optical centre O. A ray through O goes out without bending.
A lens has two foci, F1 and F2. Measure distances from the optical centre, with the same sign convention. f is positive for a convex lens and negative for a concave lens.
The lens formula is 1/v − 1/u = 1/f. Magnification is m = v/u = h′/h. The minus of the mirror formula is not here. A real image forms on the other side of the lens, so v is positive. A virtual image on the same side gives a negative v.
Power P = 1/f, with f in metres. The unit is the dioptre. +2.0 D means a convex lens and f = +0.50 m. For lenses in contact, P = P1 + P2.
Activity 9.11 — the paper burns againActivity
Turn a convex lens toward the Sun and make a sharp bright spot on paper. After a while the paper smokes and may burn. The sun’s parallel rays gathered at the focus of the lens. The distance from the lens to that spot is the approximate focal length. The caution is the same as in Activity 9.2 with the concave mirror.
Activity 9.12 — five lines and a candleActivity
Find the approximate f. On a long table draw five parallel lines, with successive gaps equal to f. Place the lens on the middle line so that the optical centre lies on the line. The lines on the two sides are F and 2F: 2F1, F1, F2 and 2F2.
First keep the candle far to the left of 2F1 and take a sharp image on a screen to the right. Then place the candle just beyond 2F1, between F1 and 2F1, at F1, and between F1 and O. Between F1 and O the image does not appear on the screen — it is on the same side, erect and enlarged.
| Object | Image | Size | Nature |
|---|---|---|---|
| Infinity | F2 | Point | Real, inverted |
| Beyond 2F1 | Between F2 and 2F2 | Diminished | Real, inverted |
| At 2F1 | At 2F2 | Same size | Real, inverted |
| Between F1 and 2F1 | Beyond 2F2 | Enlarged | Real, inverted |
| At F1 | Infinity | None | — |
| Between F1 and O | Same side | Enlarged | Virtual, erect |
Worked example — unit cmExample
Question: An object 2.0 cm high is 15 cm from a convex lens. The focal length is 10 cm. Where is the image, what is it like, and how tall is it?
Given: h = +2.0 cm, u = −15 cm, f = +10 cm. The lens is convex, so f is positive. The object is on the left, so u is negative.
Formula: 1/v − 1/u = 1/f
Substitute: 1/v = 1/f + 1/u = 1/10 + 1/(−15) = 1/10 − 1/15
= 3/30 − 2/30 = 1/30
v = +30 cm
Magnification: m = v/u = (+30 cm)/(−15 cm) = −2
h′ = m × h = (−2) × (+2.0 cm) = −4.0 cm
The image is 30 cm on the other side of the lens. It is real, inverted and twice as tall.
10-second revision
- Do not look at the Sun through the lens; the paper burns at the focus
- Lens formula 1/v − 1/u = 1/f and m = v/u
- In the example v = +30 cm and h′ = −4.0 cm
Board tip · BSEBBoard tip
Do not swap the signs of the mirror and lens formulas. The lens has a minus in the middle: 1/v − 1/u.
Board tip · CBSEBoard tip
CBSE asks for the unit. Give distances in cm, and if power is asked convert f to metres and write dioptre.
Check your understandingall correct = mastery ★
1
The correct caution while using a convex lens with the Sun is —
💡 Hint:
Activity 9.11.
Explanation:
The eyes can be damaged. Watch the spot on the paper, not the Sun.
2
If the object is at 2F1 of a convex lens, the image is at 2F2 and of the same size.
Explanation:
True — and it is real and inverted.
3
The lens formula is 1/v − 1/u = ______.
💡 Hint:
In the mirror both terms are added.
Explanation:
The lens formula is 1/v − 1/u = 1/f.
4
In the worked example the height of the image is —
💡 Hint:
m = −2 and h = +2.0 cm.
Explanation:
h′ = −4.0 cm. The minus sign means an inverted image. The place is v = +30 cm.
5
Define 1 dioptre. What kind of lens is +1.5 D and what is its focal length?
Model answer (board format)
1 dioptre is the power of a lens whose focal length is 1 metre. P = 1/f. +1.5 D is a convex, converging lens. f = 1/1.5 = 0.67 m, about 67 cm.
Check your answer:
Concave lens — Activity 9.13
अवतल लेंस — क्रियाकलाप 9.13 · NCERT Table 9.5 · Activity 9.13
Activity 9.13 — a candle and a concave lensActivity
Place a concave lens on a stand. Keep a burning candle on one side. Look through the lens from the other side. Try to catch the image on a screen.
The screen stays blank. The image is seen only in the lens — virtual, erect and diminished. Move the candle away and the image becomes smaller. Taken very far, it becomes point-sized and seems to lie toward the focus. Whatever the place, a concave lens does not give an enlarged or inverted image.
| Object | Image | Size | Nature |
|---|---|---|---|
| Infinity | At F1 | Point-sized | Virtual, erect |
| Between infinity and O | Between F1 and O | Diminished | Virtual, erect |
Negative powerNotes
A concave lens spreads rays. In the sign convention its f is negative, so the power is negative too. P = −2.0 D means f = 1/(−2.0) = −0.50 m = −50 cm. It is a diverging lens.
A convex lens with one half blackened still forms a complete image, only dimmer, because rays from the open half still come from every point. Clay is opaque, so it cannot make a lens. To read small letters, choose a convex lens of short focal length, not a concave lens.
Worked exampleExample
Question: Why is a sharp image of the candle not found when a screen is placed on the other side of a concave lens?
Answer: The lens spreads the rays. They do not meet on the other side; they appear to come from the focus on the same side. The image is virtual. A virtual image is not caught on a screen.
10-second revision
- A concave lens always gives a virtual, erect and diminished image
- The image is not obtained on a screen
- P is negative; −2.0 D means f = −50 cm
Board tip · BSEBBoard tip
Do not swap the tables of a convex and a concave lens. The concave lens has only two rows, and both are virtual.
Board tip · CBSEBoard tip
In CBSE, a mirror and a lens each of f = −15 cm are both concave. The minus sign marks the front side for the mirror and the diverging side for the lens.
Check your understandingall correct = mastery ★
1
The image in a concave lens is always —
💡 Hint:
Activity 9.13. The screen stays blank.
Explanation:
In every position the image is virtual, erect and diminished.
2
The power of a concave lens is positive.
Explanation:
False — f is negative, so P = 1/f is negative too.
3
The focal length of a −2.0 D lens is ______ m.
💡 Hint:
f = 1/P, and P is negative.
Explanation:
f = 1/(−2.0) = −0.50 m. This is a concave lens.
4
The suitable lens for reading small letters in a dictionary is —
💡 Hint:
A magnifier is convex, with more power at a smaller f.
Explanation:
A convex lens of 5 cm is a magnifier of greater power. A concave lens gives a smaller image.
5
A mirror of focal length −15 cm and a lens of the same focal length are of which types?
Model answer (board format)
Both are concave. For the mirror the minus sign says the focus is in front. For the lens the minus sign says the lens is diverging. A convex mirror and a convex lens have positive focal length.
Check your answer:
❓ Full question bank — with answers and explanations — 66 questions
Pick a type. The 49 lesson checks are separate — each lesson has as many as its topic needs. All correct earns mastery ★.
BSEB modelpractice · not annual60 tried · 0 correctMultiple choiceMCQ140 tried · 0 correctTrue / falseTrue / false80 tried · 0 correctFill in the blanksFill80 tried · 0 correctMatchMatch20 tried · 0 correctAssertion–reasonAssertion–reason40 tried · 0 correctBalancingBalancing40 tried · 0 correctIdentifyIdentify20 tried · 0 correctShort and longVSA, SA, LA120 tried · 0 correctCBSE-stylenot a PYQ60 tried · 0 correct
No question is marked as a verified past paper. The BSEB set is a model for practice. CBSE items are CBSE-style, not a copy of any year’s paper.
Multiple choice
0/14Pick one option. A wrong try brings a hint.
1
The inward surface of a spoon, held close, shows the face —
💡 Hint:
Activity 9.1.
Explanation:
A close concave surface gives an erect, enlarged image.
2
If R = 20 cm, the size of f is —
💡 Hint:
R = 2f.
Explanation:
f = R/2 = 10 cm.
3
A concave mirror forms a virtual and enlarged image when the object is —
💡 Hint:
The last row of the table.
Explanation:
Only between P and F is the image virtual, erect and enlarged.
4
The mirror in a vehicle headlight is —
💡 Hint:
A parallel beam is needed.
Explanation:
A concave mirror makes a parallel beam from a bulb kept at the focus.
5
A convex mirror is good for looking behind because —
💡 Hint:
Activities 9.5 and 9.6.
Explanation:
An erect diminished image and a wide field are both reasons.
6
m = +1 for a plane mirror says that the image is —
💡 Hint:
A plus sign is an erect image.
Explanation:
The size is equal and the image is erect.
7
However far you stand, the image is erect. The mirror is —
💡 Hint:
A concave mirror is not erect at every distance.
Explanation:
Both plane and convex mirrors give an erect image at every distance.
8
The vanished coin is seen again when water is poured into the bowl, because —
💡 Hint:
Activity 9.8.
Explanation:
The coin does not move. A ray bends and reaches the eye.
9
The ray leaving a glass slab —
💡 Hint:
The bending at the two faces is opposite.
Explanation:
The emergent ray stays parallel and shifts sideways.
10
If n = 1.50 and c = 3 × 10^8 m/s, the speed in glass is —
💡 Hint:
v = c/n.
Explanation:
v = 3 × 10^8 / 1.50 = 2 × 10^8 m/s.
11
A lens cannot be made of —
💡 Hint:
An opaque material.
Explanation:
Clay is opaque, so it cannot make a lens.
12
To get a real image the same size as the object from a convex lens, place the object —
💡 Hint:
The same-size row of the table.
Explanation:
If the object is at 2F1, the image is at 2F2 and of the same size.
13
A mirror of f = −15 cm and a lens of the same f are —
💡 Hint:
The minus sign.
Explanation:
Both are concave. A convex surface has a positive focal length.
14
To read the small letters of a dictionary, choose —
💡 Hint:
A magnifier is convex, and a shorter f means more power.
Explanation:
A convex lens of focal length 5 cm is suitable.
True or false
0/81
In Activity 9.2 it is safe to look at the Sun in the mirror.
Explanation:
False — the eyes can be damaged. Watch the spot on the paper.
2
For a small aperture the focus lies midway between the pole and the centre of curvature.
Explanation:
True — because R = 2f.
3
A convex mirror can form a real enlarged image on a screen.
Explanation:
False — the image is always virtual, erect and diminished.
4
In a plane mirror the image is as far behind as the object is in front.
Explanation:
True — and the size is equal.
5
In refraction, a ray from a denser into a rarer medium bends towards the normal.
Explanation:
False — it bends away from the normal. It bends towards the normal when it goes from rarer to denser.
6
At normal incidence a glass slab does not bend the ray.
Explanation:
True — in Activity 9.9 the line does not look bent at the edges. From above it looks raised.
7
The focal length of a convex lens is negative.
Explanation:
False — f of a convex lens is positive. f of a concave lens is negative.
8
A concave lens gives an erect and diminished image at every position.
Explanation:
True — in Activity 9.13 the image is not caught on a screen.
Fill in the blanks
0/81
The mirror formula is 1/v + 1/u = ______.
💡 Hint:
The mirror formula is 1/v + 1/u = 1/f.
Explanation:
In the lens the middle sign is minus.
2
The magnification of a mirror is m = ______.
💡 Hint:
m = −v/u.
Explanation:
The minus sign is part of the formula.
3
The magnification of a lens is m = ______.
💡 Hint:
m = v/u.
Explanation:
The mirror’s minus is not here.
4
The unit of power is the ______.
💡 Hint:
The unit is the dioptre.
Explanation:
f is in metres.
5
Write Snell’s law as n = sin i / ______.
💡 Hint:
n = sin i / sin r.
Explanation:
r is the angle of refraction.
6
The refractive index of water is about ______.
💡 Hint:
The n of water is about 1.33.
Explanation:
In the table ice is 1.31 and water is 1.33.
7
The focal length of a +2.0 D lens is ______ m.
💡 Hint:
f = 1/2.0 = 0.50 m. The lens is convex.
Explanation:
f = 1/P.
8
A ray through the optical centre does not ______.
💡 Hint:
It goes out without bending.
Explanation:
It goes straight through O.
Match
0/21
Match the device with the job.
Column B: A. Headlight beam · B. Rear-view mirror · C. Reading small letters · D. Always a small erect image
1. Concave mirror
2. Convex mirror
3. Convex lens
4. Concave lens
Explanation:
Headlight concave, rear-view convex, magnifier a convex lens, always-small image a concave lens.
2
Match the formula with its use.
Column B: A. Spherical mirror · B. Mirror magnification · C. Spherical lens · D. Refractive index
1. 1/v + 1/u = 1/f
2. m = −v/u
3. 1/v − 1/u = 1/f
4. n = c/v
Explanation:
The first is the mirror formula, the second mirror m, the third the lens formula, the fourth refractive index.
Assertion–reason
0/4Check both statements, then see whether the reason explains the assertion.
1
Assertion (A): A convex mirror is used as a rear-view mirror.
Reason (R): It gives an erect image and a wide field.
Explanation:
Both are true and R explains A.
2
Assertion (A): In Activity 9.2 the paper can catch fire.
Reason (R): To see the focus one should look at the Sun in the mirror with the eye.
Explanation:
A is true. R is false — do not look at the Sun in the mirror. Watch the spot on the paper.
3
Assertion (A): The emergent ray of a slab is parallel to the incident ray.
Reason (R): The bending at the two parallel faces is equal and opposite.
Explanation:
Both are true and R is the correct reason.
4
Assertion (A): A concave lens forms a real enlarged image on a screen.
Reason (R): A concave lens spreads rays.
Explanation:
A is false. R is true — the image stays virtual, erect and diminished.
Balance the equation
0/4This chapter has no chemical equation. The tray below is only coefficient practice, not an optics result.
1
This is coefficient practice 1, not a result of this chapter. This light chapter has no chemical equation.
H2 + O2 → H2O
Explanation: 2H2 + O2 → 2H2O — coefficient practice for water. Do not treat it as an optics result.
2
This is coefficient practice 2, not a result of this chapter. This light chapter has no chemical equation.
H2 + O2 → H2O
Explanation: 2H2 + O2 → 2H2O — coefficient practice for water. Do not treat it as an optics result.
3
This is coefficient practice 3, not a result of this chapter. This light chapter has no chemical equation.
H2 + O2 → H2O
Explanation: 2H2 + O2 → 2H2O — coefficient practice for water. Do not treat it as an optics result.
4
This is coefficient practice 4, not a result of this chapter. This light chapter has no chemical equation.
H2 + O2 → H2O
Explanation: 2H2 + O2 → 2H2O — coefficient practice for water. Do not treat it as an optics result.
Classify
0/21
Place each use as a concave mirror, a convex mirror or a plane mirror.
Solar furnace
Vehicle side mirror
Ordinary mirror with m = +1
Explanation:
Solar furnace concave, side mirror convex, m = +1 plane.
2
Place each image as real, virtual-enlarged, or virtual-diminished.
Concave, object at C
Concave, object between P and F
Convex, object anywhere in front
Explanation:
At C the image is real. Between P and F it is virtual and enlarged. A convex mirror is always virtual and diminished.
Very short answer
0/51
Write the relation of R and f for a spherical mirror.
Model answer (board format)
R = 2f. For a small aperture the focus lies midway between the pole and the centre of curvature.
Check your answer:
2
Write the mirror formula.
Model answer (board format)
1/v + 1/u = 1/f.
Check your answer:
3
What is 1 dioptre?
Model answer (board format)
The power of a lens of focal length 1 metre is 1 dioptre. P = 1/f, with f in metres.
Check your answer:
4
Write Snell’s law.
Model answer (board format)
For a given colour and a given pair of media, sin i / sin r stays constant. That constant is called the refractive index.
Check your answer:
5
Write the caution of Activity 9.2 in one sentence.
Model answer (board format)
Do not look at the Sun directly or into a mirror reflecting sunlight; the eyes can be damaged.
Check your answer:
Short answer
0/41
An object is 10 cm from a convex mirror. The focal length of the mirror is 15 cm. Find the place and nature of the image. Keep the unit cm.
Model answer (board format)
u = −10 cm, f = +15 cm. Formula 1/v + 1/u = 1/f. 1/v = 1/15 − 1/(−10) = 1/15 + 1/10 = 2/30 + 3/30 = 5/30 = 1/6. v = +6 cm. The image is 6 cm behind the mirror, virtual and erect. m = −v/u = −(6)/(−10) = +0.6, so it is also diminished.
Check your answer:
2
A concave lens has a focal length of 15 cm. The image is 10 cm from the lens. How far is the object? Keep the unit cm.
Model answer (board format)
f = −15 cm, v = −10 cm, because the image of a concave lens is on the object’s side. 1/v − 1/u = 1/f. 1/u = 1/v − 1/f = 1/(−10) − 1/(−15) = −1/10 + 1/15 = −3/30 + 2/30 = −1/30. u = −30 cm. The object is 30 cm from the lens. m = v/u = (−10)/(−30) = +1/3.
Check your answer:
3
What do Activities 9.7 and 9.8 both show? Write one sentence for each.
Model answer (board format)
In 9.7 the coin in the bucket looked raised by refraction, so the hand could not pick it in one try. In 9.8 the hidden coin appeared raised when water was poured and was seen again. In both, the real place did not change.
Check your answer:
4
A concave mirror has a focal length of 15 cm. An erect image is wanted. In what range should the object distance lie? What will the image be like?
Model answer (board format)
The object should be between the pole and the focus, that is between 0 and 15 cm from the mirror. The image will be virtual, erect and larger than the object, behind the mirror.
Check your answer:
Long answer
0/31
An object 4.0 cm high is 25 cm from a concave mirror and f = 15 cm. Find the place of the screen, and the nature and height of the image. Write the unit at every step.
Model answer (board format)
u = −25 cm, f = −15 cm, h = +4.0 cm. 1/v + 1/u = 1/f. 1/v = 1/(−15) − 1/(−25) = −1/15 + 1/25 = −5/75 + 3/75 = −2/75. v = −37.5 cm. The screen is 37.5 cm in front. m = −v/u = −(−37.5)/(−25) = −1.5. h′ = −1.5 × 4.0 cm = −6.0 cm. The image is real, inverted and enlarged.
Check your answer:
2
Write the three ray rules for a convex lens and say whether a complete image is formed if half the lens is blackened.
Model answer (board format)
A ray parallel to the axis passes through the focus on the other side after refraction. A ray through the focus comes out parallel to the axis after refraction. A ray through the optical centre does not bend. If half is blackened, rays from every point still come through the open part, so a complete image is formed; it is only dimmer because less light passes.
Check your answer:
3
Compare the mirror formula and the lens formula. Also write two points of the sign convention.
Model answer (board format)
The mirror formula is 1/v + 1/u = 1/f and m = −v/u. The lens formula is 1/v − 1/u = 1/f and m = v/u. In both, the object is on the left, so u is negative. Distances are measured from the pole for a mirror and from the optical centre for a lens. f is negative for a concave mirror and a concave lens; f is positive for both convex ones.
Check your answer:
BSEB model paper · practice
0/6This model set is for practice. It is not an annual paper of any year.
1
A shaving mirror is —
💡 Hint:
A large erect face.
Explanation:
A concave mirror shows the face enlarged and erect between P and F.
2
The speed of light in water, compared with kerosene, is —
💡 Hint:
Water 1.33, kerosene 1.44.
Explanation:
The speed is greater at a smaller refractive index. Light is faster in water.
3
In R = 2f, if R = 30 cm then f = ______ cm.
💡 Hint:
f = 15 cm.
Explanation:
Take half.
4
What is lateral displacement?
Model answer (board format)
The ray leaving a glass slab stays parallel to the incident ray, but it shifts sideways. That shift is called lateral displacement.
Check your answer:
5
Write two of the uses of a concave mirror and give one reason for each.
Model answer (board format)
In a headlight a source at the focus gives a strong parallel beam. In a shaving mirror the face, kept between P and F, looks erect and enlarged. A solar furnace gathers the sun’s rays at the focus to make heat.
Check your answer:
6
Write the rules of the sign convention and say why f of a concave mirror is negative.
Model answer (board format)
The object is placed on the left. Distances are measured from the pole for a mirror and from the optical centre for a lens. The left side is negative and the right side is positive. Above the axis is positive and below is negative. The focus of a concave mirror is in front, that is on the left. So f is written as negative.
Check your answer:
CBSE-style questions
0/6These are competency-based practice questions. This is not a past paper.
1
A student burns paper to measure the focus and also looks at the Sun in the mirror. The mistake is —
💡 Hint:
Caution of 9.2.
Explanation:
Burning the paper is part of the experiment. The eye should not be put in the reflected ray of the Sun.
2
A convex lens with one half blackened, of an object, forms —
💡 Hint:
Rays still come through the open part.
Explanation:
A complete image is formed, because rays from every point of the object still pass through the open half. Less light makes the image dimmer.
3
Assertion (A): A lens cannot be made of clay.
Reason (R): The material of a lens must be transparent.
Explanation:
Both are true and R is the correct reason.
4
Assertion (A): The refractive index of diamond is 2.42.
Reason (R): Diamond is optically denser than air.
Explanation:
Both are true, but R alone does not fully explain the number 2.42. The number says the speed in air is 2.42 times the speed in diamond. Being denser gives the direction, not the factor.
5
A doctor puts lenses of +2.0 D and +0.25 D together. Find the total power and the total focal length. Is the lens convex or concave?
Model answer (board format)
In contact, P = P1 + P2 = +2.0 + +0.25 = +2.25 D. f = 1/P = 1/2.25 m = 0.44 m. The power is positive, so the combination behaves as a convex, converging lens.
Check your answer:
6
A boy tries to pick a coin in a pond and the hand comes out above the coin. Write the reason from Activity 9.7. Was the coin really higher?
Model answer (board format)
No. A ray coming from water into air bends, so the coin looks raised. The real depth is greater. In Activity 9.7 the coin in the bucket is missed in one try for the same reason.
Check your answer:
🏛️ Board exam corner — Bihar Board (BSEB)— CBSE
Switch board with BSEB | CBSE above. The lessons follow the same NCERT chapter.
BSEB model · practiceBoard tip
This page has no verified annual-exam question, because no source page has been added. The model set below is practice in the board pattern.
🏛️ Model questions on one page →
The verified label will be used only when a source page for the question is available.
CBSE-style · competency-based
These are case and assertion-reason practice items. Do not treat them as past CBSE questions.
🔁 Spaced review — today’s questions
Wrong questions return soon; correct ones return after a few days.
🧠 What you learned + equation sheet
What you learned
- Both laws of reflection hold for spherical mirrors too: angle of incidence equals angle of reflection, and the three rays lie in one plane.
- A concave mirror gathers sunlight at one point. Do not look at the Sun or at its reflected ray. For a small aperture, R = 2f.
- A concave mirror gives a virtual, erect and enlarged image only when the object is between the pole and the focus.
- Mirror formula 1/v + 1/u = 1/f and m = −v/u. The object distance u is always negative. f is negative for a concave mirror and positive for a convex mirror.
- In refraction a ray from rarer to denser bends towards the normal. The ray leaving a slab stays parallel to the incident ray. n = sin i / sin r.
- Lens formula 1/v − 1/u = 1/f and m = v/u. Power P = 1/f with f in metres, unit dioptre. A concave lens always gives an erect, diminished image.
| What | Keep this |
|---|---|
| Mirror formula | 1/v + 1/u = 1/f |
| Mirror magnification | m = −v/u |
| Focus and radius | R = 2f |
| Lens formula | 1/v − 1/u = 1/f |
| Lens magnification | m = v/u |
| Snell | n = sin i / sin r |
The notes are original writing. The textbook was used only for activity order and numbers. “Verified” will be used only on a question that has a source page.