💡 Refraction of Light is a high-weightage chapter in AMU — 2–3 questions every year. Snell's law, refractive index numericals, lens formula, power of lens, dispersion, and total internal reflection are the most tested topics. This mega guide covers everything with 18+ PYQs, 18+ solved numericals, and step-by-step solutions. Let's ace it!
1) What is Refraction? — Complete Explanation
When light travels from one transparent medium to another, it bends at the boundary. This bending of light is called refraction. The bending occurs because light changes speed when it moves from one medium to another.
Cause of refraction:
Light travels at different speeds in different media
In vacuum / air: speed = 3 × 10⁸ m/s (maximum)
In water: speed ≈ 2.25 × 10⁸ m/s
In glass: speed ≈ 1.97 × 10⁸ m/s
When speed changes → direction changes → bending
🟡 Senior's Tip — Which way does it bend?
• Light going from rarer → denser (e.g., air → water/glass): speed DECREASES → bends TOWARD the normal
• Light going from denser → rarer (e.g., water/glass → air): speed INCREASES → bends AWAY FROM the normal
• If light strikes the boundary at 90° (normal incidence): it passes through WITHOUT bending (i = 0, r = 0)
• Light going from rarer → denser (e.g., air → water/glass): speed DECREASES → bends TOWARD the normal
• Light going from denser → rarer (e.g., water/glass → air): speed INCREASES → bends AWAY FROM the normal
• If light strikes the boundary at 90° (normal incidence): it passes through WITHOUT bending (i = 0, r = 0)
Real-Life Examples of Refraction:
- Pencil in water: A pencil placed in a glass of water appears broken/bent at the water surface — light from the underwater part bends as it exits water into air
- Pool appears shallower: A swimming pool looks shallower than its actual depth — light from the bottom refracts at the water surface, making the bottom appear raised
- Coin in a cup: Place a coin in a cup and move back until it disappears. Pour water — the coin becomes visible again! (Water refraction changes the apparent position)
- Fish in water: A fish in water appears at a higher position than its actual location
- Lemon in tea: A lemon slice in a glass of tea looks larger and displaced
🔥 AMU PYQ: When light travels from air to glass, it bends:
(A) Away from the normal (B) Toward the normal (C) Does not bend (D) Along the boundary
Ans: B (rarer → denser, speed decreases, bends toward normal)
(A) Away from the normal (B) Toward the normal (C) Does not bend (D) Along the boundary
Ans: B (rarer → denser, speed decreases, bends toward normal)
2) Laws of Refraction — Snell's Law ⭐
First Law of Refraction:
The incident ray, the refracted ray, and the normal at the point of incidence all lie in the SAME plane
Second Law of Refraction — Snell's Law:
n₁ × sin i = n₂ × sin r
OR equivalently: sin i / sin r = n₂ / n₁ = constant = n₂₁
n₁ = refractive index of first medium
n₂ = refractive index of second medium
i = angle of incidence (in first medium)
r = angle of refraction (in second medium)
Alternative form — using speeds:
sin i / sin r = v₁ / v₂ = n₂ / n₁
v₁ = speed of light in first medium
v₂ = speed of light in second medium
🟡 Senior's Tip — Snell's law in words:
"The ratio of the sine of the angle of incidence to the sine of the angle of refraction is constant for a given pair of media." This constant is called the relative refractive index of the second medium with respect to the first (n₂₁).
"The ratio of the sine of the angle of incidence to the sine of the angle of refraction is constant for a given pair of media." This constant is called the relative refractive index of the second medium with respect to the first (n₂₁).
Solved Example — Snell's Law:
Light enters water (n = 1.33) from air (n = 1) at an angle of incidence of 45°. Find the angle of refraction.
Light enters water (n = 1.33) from air (n = 1) at an angle of incidence of 45°. Find the angle of refraction.
n₁ sin i = n₂ sin r
1 × sin 45° = 1.33 × sin r
0.7071 = 1.33 × sin r
sin r = 0.7071 / 1.33 = 0.5317
r = sin⁻¹(0.5317) = ≈ 32.1°
🔥 AMU PYQ: Snell's law is expressed as:
(A) n₁ sin r = n₂ sin i (B) n₁ sin i = n₂ sin r (C) sin i / sin r = n₁/n₂ (D) Both B and C
Ans: D (n₁ sin i = n₂ sin r is the same as sin i/sin r = n₂/n₁)
(A) n₁ sin r = n₂ sin i (B) n₁ sin i = n₂ sin r (C) sin i / sin r = n₁/n₂ (D) Both B and C
Ans: D (n₁ sin i = n₂ sin r is the same as sin i/sin r = n₂/n₁)
3) Refractive Index — Complete Details
Absolute Refractive Index (n):
n = c / v
c = speed of light in vacuum = 3 × 10⁸ m/s
v = speed of light in the medium
n is a PURE NUMBER (no unit)
n ≥ 1 always (v ≤ c, so n ≥ 1)
| Medium | Refractive Index (n) | Speed of light (×10⁸ m/s) | Optical density |
|---|---|---|---|
| Vacuum / Air (≈) | 1.00 | 3.00 | Rarest |
| Ice | 1.31 | 2.29 | — |
| Water | 1.33 | 2.25 | Rarer |
| Alcohol | 1.36 | 2.21 | — |
| Kerosene | 1.44 | 2.08 | — |
| Glass (crown) | 1.52 | 1.97 | Denser |
| Glass (flint) | 1.62 | 1.85 | Denser |
| Ruby | 1.71 | 1.75 | — |
| Diamond | 2.42 | 1.24 | Densest |
🟡 Senior's Tip — Key facts about refractive index:
• Higher n → slower light → more bending
• Diamond (n = 2.42) has the highest refractive index among common substances → light travels slowest in diamond
• Diamond sparkles due to Total Internal Reflection — critical angle is only ~24°
• Optical density ≠ Mass density. E.g., oil has higher optical density than water but lower mass density
• Refractive index depends on: nature of medium, colour/wavelength of light (dispersion!)
• n is slightly different for different colours — this is why a prism splits white light
• Higher n → slower light → more bending
• Diamond (n = 2.42) has the highest refractive index among common substances → light travels slowest in diamond
• Diamond sparkles due to Total Internal Reflection — critical angle is only ~24°
• Optical density ≠ Mass density. E.g., oil has higher optical density than water but lower mass density
• Refractive index depends on: nature of medium, colour/wavelength of light (dispersion!)
• n is slightly different for different colours — this is why a prism splits white light
Relative Refractive Index:
n₂₁ = n₂ / n₁ = v₁ / v₂
n₂₁ = refractive index of medium 2 w.r.t. medium 1
If n₂ > n₁: medium 2 is optically denser → light bends toward normal
If n₂ < n₁: medium 2 is optically rarer → light bends away from normal
🔥 AMU PYQ: Refractive index of diamond is:
(A) 1.33 (B) 1.52 (C) 2.42 (D) 1.00
Ans: C (2.42 — highest among common substances)
(A) 1.33 (B) 1.52 (C) 2.42 (D) 1.00
Ans: C (2.42 — highest among common substances)
🔥 AMU PYQ: Speed of light in water is (n = 1.33):
Ans: v = c/n = 3 × 10⁸ / 1.33 = 2.26 × 10⁸ m/s
Ans: v = c/n = 3 × 10⁸ / 1.33 = 2.26 × 10⁸ m/s
4) Principle of Reversibility of Light
The principle of reversibility states that if the path of light is reversed, it travels back along the same path. In other words, if light goes from A → B through a series of media, it will follow the same path B → A in reverse.
Mathematically:
n₁₂ = 1 / n₂₁
If glass has n = 1.5 w.r.t. air, then air has n = 1/1.5 = 0.667 w.r.t. glass
Since n < 1 is impossible (v > c?), we instead say:
n_air/wrt/glass = 1 / n_glass/wrt/air = 1/1.5
🟡 Senior's Tip — Application:
If you know the refractive index from air to water (1.33), you automatically know the refractive index from water to air:
n_water→air = 1 / 1.33 = 0.75
This is useful in Snell's law when light goes from water → air.
If you know the refractive index from air to water (1.33), you automatically know the refractive index from water to air:
n_water→air = 1 / 1.33 = 0.75
This is useful in Snell's law when light goes from water → air.
5) Refraction Through a Rectangular Glass Slab — Lateral Shift
When a ray of light passes through a rectangular glass slab, it undergoes refraction twice — once entering the glass and once emerging from it.
Complete path through a glass slab:
1. Air → Glass (at first face): bends TOWARD normal (rarer → denser)
2. Travels through glass (straight line inside the slab)
3. Glass → Air (at opposite face): bends AWAY FROM normal (denser → rarer)
The emergent ray is PARALLEL to the incident ray, but slightly displaced sideways
Lateral Shift / Displacement:
The perpendicular distance between the incident ray (extended) and the emergent ray is called the lateral shift or lateral displacement.
Lateral shift = t × sin(i − r) / cos r
t = thickness of the glass slab
i = angle of incidence
r = angle of refraction
🟡 Senior's Tip — Factors affecting lateral shift:
• Increases with thickness of slab (t)
• Increases with angle of incidence (i)
• Increases with refractive index of the material (more bending → more shift)
• For normal incidence (i = 0), lateral shift = 0 (light passes straight through)
• Increases with thickness of slab (t)
• Increases with angle of incidence (i)
• Increases with refractive index of the material (more bending → more shift)
• For normal incidence (i = 0), lateral shift = 0 (light passes straight through)
🔥 AMU PYQ: When light passes through a rectangular glass slab, the emergent ray is:
(A) Parallel to incident ray (B) Perpendicular to incident ray (C) Deviated (D) Dispersed
Ans: A (emergent ray is parallel to incident ray, just displaced sideways)
(A) Parallel to incident ray (B) Perpendicular to incident ray (C) Deviated (D) Dispersed
Ans: A (emergent ray is parallel to incident ray, just displaced sideways)
6) Real and Apparent Depth ⭐
When an object is placed in a denser medium (like water), it appears to be at a shallower depth than its actual depth. This is due to refraction of light at the interface.
Key formula:
Apparent depth = Real depth / n
OR: n = Real depth / Apparent depth
n = refractive index of the denser medium w.r.t. rarer medium
🟡 Senior's Tip — "The pool always looks shallower":
• When you look at a swimming pool, your brain assumes light travels in a straight line
• But the light from the bottom bends at the water surface → your brain thinks it's coming from a higher point
• Apparent depth < Real depth → pool looks shallower than it actually is
• This is why you should NEVER dive into an unfamiliar water body — it's always deeper than it looks!
• When you look at a swimming pool, your brain assumes light travels in a straight line
• But the light from the bottom bends at the water surface → your brain thinks it's coming from a higher point
• Apparent depth < Real depth → pool looks shallower than it actually is
• This is why you should NEVER dive into an unfamiliar water body — it's always deeper than it looks!
Solved Example: A swimming pool appears to be 1.5 m deep. If n_water = 1.33, find actual depth.
n = Real depth / Apparent depth
1.33 = Real depth / 1.5
Real depth = 1.33 × 1.5 = 2.0 m
🔥 AMU PYQ: A fish in water appears at a depth of 15 cm. If n = 1.33, its actual depth is:
(A) 15 cm (B) 20 cm (C) 11.3 cm (D) 25 cm
Ans: B (Real depth = n × apparent = 1.33 × 15 = 19.95 ≈ 20 cm)
(A) 15 cm (B) 20 cm (C) 11.3 cm (D) 25 cm
Ans: B (Real depth = n × apparent = 1.33 × 15 = 19.95 ≈ 20 cm)
7) Total Internal Reflection (TIR) ⭐
Total Internal Reflection is one of the most fascinating and important optical phenomena. It occurs when light traveling in a denser medium strikes the boundary with a rarer medium at an angle greater than the critical angle.
Conditions for TIR — BOTH must be satisfied:
1. Light must travel from DENSER medium to RARER medium (n₁ > n₂)
2. Angle of incidence (i) must be > Critical angle (C)
Critical Angle (C):
The angle of incidence in the denser medium for which the angle of refraction in the rarer medium is 90°. At this angle, the refracted ray grazes the boundary.
Formula for critical angle:
Critical angles to memorize:
sin C = n₂ / n₁
If the rarer medium is air/vacuum (n₂ = 1):
sin C = 1 / n₁
C = sin⁻¹(1/n₁)
Critical angles to memorize:
Water → air: C = sin⁻¹(1/1.33) = sin⁻¹(0.752) ≈ 49°
Glass → air: C = sin⁻¹(1/1.52) = sin⁻¹(0.658) ≈ 42°
Diamond → air: C = sin⁻¹(1/2.42) = sin⁻¹(0.413) ≈ 24°
🟡 Senior's Tip — Why diamond sparkles:
Diamond has a VERY small critical angle (~24°). This means that once light enters a diamond, it gets trapped inside — it undergoes multiple total internal reflections before finally emerging. This multiple TIR is what gives diamonds their brilliant "sparkle" or "fire." Diamond cutters cut the facets at precise angles to maximize this effect!
Diamond has a VERY small critical angle (~24°). This means that once light enters a diamond, it gets trapped inside — it undergoes multiple total internal reflections before finally emerging. This multiple TIR is what gives diamonds their brilliant "sparkle" or "fire." Diamond cutters cut the facets at precise angles to maximize this effect!
Applications of TIR:
| Application | How TIR is used |
|---|---|
| Optical fibres | Light signals travel through thin glass/plastic fibres by repeated TIR. Used in: internet communication, telephone, cable TV, medical endoscopy. Extremely high data transmission capacity! |
| Diamond sparkle | Small critical angle (~24°) → light undergoes many internal reflections → brilliant shine |
| Mirage | On hot roads, air near the ground is hotter (rarer) than air above (denser). Light from the sky bends upward by TIR → we see a false "water" reflection on the road |
| Endoscopy | Optical fibres carry light into the body and bring back images — allows non-invasive medical examination |
| Binoculars & Periscopes | Use prisms with TIR to reflect light (more efficient than mirror reflection as there's no absorption) |
🔥 AMU PYQ: Total Internal Reflection occurs when light travels from:
(A) Rarer to denser (B) Denser to rarer with i > C (C) Denser to rarer with i < C (D) Any medium
Ans: B
(A) Rarer to denser (B) Denser to rarer with i > C (C) Denser to rarer with i < C (D) Any medium
Ans: B
🔥 AMU PYQ: The critical angle for glass-air is about:
(A) 24° (B) 42° (C) 49° (D) 90°
Ans: B (glass → air C ≈ 42°)
(A) 24° (B) 42° (C) 49° (D) 90°
Ans: B (glass → air C ≈ 42°)
8) Lenses — Convex and Concave ⭐
A lens is a transparent medium bounded by two curved surfaces (usually spherical). Lenses work on the principle of refraction. They are of two types:
| Property | Convex Lens (Converging) | Concave Lens (Diverging) |
|---|---|---|
| Shape | Thicker at centre, thinner at edges | Thinner at centre, thicker at edges |
| Effect on light | Converges parallel rays to a point | Diverges parallel rays (appear to come from a point) |
| Focus | Real (on opposite side of light) | Virtual (on same side as light) |
| Focal length | Positive (+ve) | Negative (−ve) |
| Image types | Real OR virtual (depends on object position) | ALWAYS virtual, erect, diminished |
| Uses | Magnifying glass, camera, microscope, telescope, hypermetropia glasses | Myopia (shortsightedness) glasses |
Lens Terminology:
• Optical Centre (O): Centre of the lens (midpoint on principal axis)
• Principal Focus (F):
— Convex: Point where parallel rays converge (real, on other side)
— Concave: Point from which parallel rays appear to diverge (virtual, same side)
• Focal Length (f): Distance from O to F
• 2F: Point at twice the focal length from O (one on each side)
9) Ray Diagrams for Lenses — Rules
Rule 1 — Ray parallel to principal axis:
After refraction, passes through F (convex) OR appears to come from F (concave)
Rule 2 — Ray passing through F (or directed towards F):
After refraction, becomes parallel to principal axis
Rule 3 — Ray passing through O (optical centre):
Passes through WITHOUT any deviation (undergoes only very slight lateral shift)
🟡 Senior's Tip — Drawing lens ray diagrams:
• Draw the lens as a vertical line with arrowheads at both ends (convex → outward, concave → inward)
• Mark O, F, and 2F on both sides
• Use any two of the 3 rules above to locate the image
• Extend diverging rays backward with dashed lines for virtual images
• Draw the lens as a vertical line with arrowheads at both ends (convex → outward, concave → inward)
• Mark O, F, and 2F on both sides
• Use any two of the 3 rules above to locate the image
• Extend diverging rays backward with dashed lines for virtual images
10) Image Formation by Convex Lens — 6 Cases
| Case | Object Position | Image Position | Nature | Size | Example use |
|---|---|---|---|---|---|
| 1 | At infinity | At F | Real, inverted | Highly diminished | Telescope objective |
| 2 | Beyond 2F | Between F and 2F (other side) | Real, inverted | Diminished | Camera |
| 3 | At 2F | At 2F (other side) | Real, inverted | Same size | — |
| 4 | Between F and 2F | Beyond 2F (other side) | Real, inverted | Enlarged | Projector, cinema |
| 5 | At F | At infinity | — | Highly enlarged | Spotlight, torch |
| 6 | Between O and F | Same side, before object | Virtual, erect | Enlarged | Magnifying glass |
🟡 Senior's Trick — Convex Lens Cases:
• Object beyond 2F → image real, inverted, diminished (camera)
• Object between F and 2F → image real, inverted, enlarged (projector)
• Object between O and F → image virtual, erect, enlarged (magnifying glass)
• Object at 2F → image real, inverted, same size at 2F
• Object beyond 2F → image real, inverted, diminished (camera)
• Object between F and 2F → image real, inverted, enlarged (projector)
• Object between O and F → image virtual, erect, enlarged (magnifying glass)
• Object at 2F → image real, inverted, same size at 2F
11) Image Formation by Concave Lens — 2 Cases
| Case | Object Position | Image Position | Nature | Size |
|---|---|---|---|---|
| 1 | At infinity | At F (same side) | Virtual, erect | Highly diminished |
| 2 | Anywhere in front | Between O and F (same side) | Virtual, erect | Diminished (m < 1) |
🟡 Senior's Tip — Concave Lens is boring (but easy!):
A concave lens ALWAYS gives: ✅ Virtual ✅ Erect ✅ Diminished image
No matter where you place the object! This is because the lens diverges rays — they can never converge to form a real image.
A concave lens ALWAYS gives: ✅ Virtual ✅ Erect ✅ Diminished image
No matter where you place the object! This is because the lens diverges rays — they can never converge to form a real image.
12) Lens Formula & Magnification ⭐
Lens formula — DIFFERENT from mirror formula:
1/f = 1/v − 1/u
f = focal length
u = object distance (from optical centre O)
v = image distance (from optical centre O)
Magnification by lens:
m = hᵢ / hₒ = v / u
hᵢ = image height, hₒ = object height
m > 0 → virtual, erect image
m < 0 → real, inverted image
|m| > 1 → enlarged, |m| = 1 → same size, |m| < 1 → diminished
Sign Convention for Lenses (Cartesian):
1. Optical centre O is the ORIGIN
2. Distances measured in direction of incident light → +ve
3. Distances measured opposite to incident light → −ve
4. u (object distance) → ALWAYS −ve (object is on incident light side)
5. f for CONVEX lens → +ve (real focus on opposite side)
6. f for CONCAVE lens → −ve (virtual focus on same side)
7. v: real image → +ve (opposite side), virtual image → −ve (same side)
8. Heights: above axis → +ve, below axis → −ve
🟡 Senior's CRITICAL Distinction — Mirror vs Lens:
Memorize this — it's the #1 mistake in exams!
Mirror formula: 1/f = 1/u + 1/v
Lens formula: 1/f = 1/v − 1/u
Mirror magnification: m = −v/u
Lens magnification: m = v/u (NO minus sign!)
Memorize this — it's the #1 mistake in exams!
13) Power of a Lens ⭐
Power of a lens:
P = 1 / f (where f is in metres)
SI unit: Dioptre (D)
1 D = 1 m⁻¹
Convex lens → P > 0 (positive power)
Concave lens → P < 0 (negative power)
Combination of lenses (in contact):
P_total = P₁ + P₂ + P₃ + ...
1/f_total = 1/f₁ + 1/f₂ + 1/f₃ + ...
This is used when two or more lenses are placed in contact
E.g., if convex (+2 D) and concave (−1 D) are combined: P = +1 D
🟡 Senior's Tip — Quick power calculations:
• f = 50 cm = 0.5 m → P = 1/0.5 = +2 D (convex lens)
• f = −25 cm = −0.25 m → P = 1/(−0.25) = −4 D (concave lens)
• P = +5 D → f = 1/5 = 0.2 m = 20 cm (convex lens)
• P = −2.5 D → f = 1/(−2.5) = −0.4 m = −40 cm (concave lens)
• f = 50 cm = 0.5 m → P = 1/0.5 = +2 D (convex lens)
• f = −25 cm = −0.25 m → P = 1/(−0.25) = −4 D (concave lens)
• P = +5 D → f = 1/5 = 0.2 m = 20 cm (convex lens)
• P = −2.5 D → f = 1/(−2.5) = −0.4 m = −40 cm (concave lens)
🔥 AMU PYQ: Power of a lens is +2 D. Its focal length is:
(A) 50 cm (B) 2 m (C) 0.5 m (D) 20 cm
Ans: A (f = 1/P = 1/2 = 0.5 m = 50 cm. Positive → convex lens)
(A) 50 cm (B) 2 m (C) 0.5 m (D) 20 cm
Ans: A (f = 1/P = 1/2 = 0.5 m = 50 cm. Positive → convex lens)
🔥 AMU PYQ: Power of a concave lens is:
(A) Always positive (B) Always negative (C) Zero (D) Can be positive or negative
Ans: B (concave lens → f negative → P negative)
(A) Always positive (B) Always negative (C) Zero (D) Can be positive or negative
Ans: B (concave lens → f negative → P negative)
14) Dispersion of Light (Prism) ⭐
When white light passes through a prism, it splits into its constituent colours — this phenomenon is called dispersion.
The visible spectrum — VIBGYOR:
Violet → Indigo → Blue → Green → Yellow → Orange → Red
(Wavelength increases from left to right: 400 nm → 700 nm)
Violet deviates the MOST (shortest λ, slows down most → bends most)
Red deviates the LEAST (longest λ, slows down least → bends least)
🟡 Senior's Tip — Why does dispersion happen?
The refractive index of glass is different for different colours.
• n_violet ≈ 1.53 (highest n → most bending)
• n_red ≈ 1.51 (lowest n → least bending)
This small difference in n causes different colours to bend by different amounts → they separate into a spectrum! This is called chromatic dispersion.
The refractive index of glass is different for different colours.
• n_violet ≈ 1.53 (highest n → most bending)
• n_red ≈ 1.51 (lowest n → least bending)
This small difference in n causes different colours to bend by different amounts → they separate into a spectrum! This is called chromatic dispersion.
Rainbow Formation — Nature's Prism:
- Raindrops act as tiny prisms
- Sunlight enters a raindrop → refracts (splits into colours) → undergoes TIR at the back of the drop → refracts again when exiting
- We see a primary rainbow at 42° from the anti-sun direction (red on outer edge, violet on inner)
- A secondary rainbow at 52° may also be visible (colours reversed: violet on outer, red on inner)
🔥 AMU PYQ: Which colour deviates the most in a prism?
(A) Red (B) Green (C) Violet (D) Yellow
Ans: C (violet deviates most — shortest wavelength)
(A) Red (B) Green (C) Violet (D) Yellow
Ans: C (violet deviates most — shortest wavelength)
🔥 AMU PYQ: Rainbow is formed due to:
(A) Reflection only (B) Refraction and TIR (C) Dispersion only (D) Both B and C
Ans: D (refraction + dispersion + total internal reflection in water droplets)
(A) Reflection only (B) Refraction and TIR (C) Dispersion only (D) Both B and C
Ans: D (refraction + dispersion + total internal reflection in water droplets)
15) PYQ Battle — 18 AMU Past Questions on Refraction
Q1. When light goes from air to glass, it bends:
(A) Away from normal (B) Toward normal (C) Doesn't bend (D) Along boundary
Ans: B
(A) Away from normal (B) Toward normal (C) Doesn't bend (D) Along boundary
Ans: B
Q2. Snell's law is:
(A) n₁ sin r = n₂ sin i (B) n₁ sin i = n₂ sin r (C) sin i/sin r = n₁/n₂ (D) Both B and C
Ans: D
(A) n₁ sin r = n₂ sin i (B) n₁ sin i = n₂ sin r (C) sin i/sin r = n₁/n₂ (D) Both B and C
Ans: D
Q3. Refractive index of diamond is:
(A) 1.33 (B) 1.52 (C) 2.42 (D) 1.00
Ans: C
(A) 1.33 (B) 1.52 (C) 2.42 (D) 1.00
Ans: C
Q4. Speed of light in water (n = 1.33) is:
Ans: v = 3×10⁸/1.33 = 2.26 × 10⁸ m/s
Ans: v = 3×10⁸/1.33 = 2.26 × 10⁸ m/s
Q5. A convex lens (f = 15 cm) has object at 10 cm. Image position?
1/v = 1/15 + 1/(−10) = 1/15 − 1/10 = −1/30
Ans: v = −30 cm (virtual, same side, enlarged, erect)
Q6. The power of a lens is −5 D. Focal length is:
Ans: f = 1/P = 1/(−5) = −0.2 m = −20 cm (concave lens)
Ans: f = 1/P = 1/(−5) = −0.2 m = −20 cm (concave lens)
Q7. Which phenomenon causes diamond sparkle?
(A) Refraction (B) Dispersion (C) TIR (D) Diffraction
Ans: C (TIR — small critical angle ~24°)
(A) Refraction (B) Dispersion (C) TIR (D) Diffraction
Ans: C (TIR — small critical angle ~24°)
Q8. Refractive index of a medium is 1.5. Speed of light in that medium is:
Ans: v = 3×10⁸/1.5 = 2 × 10⁸ m/s
Ans: v = 3×10⁸/1.5 = 2 × 10⁸ m/s
Q9. A concave lens always forms an image that is:
(A) Real and inverted (B) Virtual and diminished (C) Real and enlarged (D) Virtual and enlarged
Ans: B (concave lens → always virtual, erect, diminished)
(A) Real and inverted (B) Virtual and diminished (C) Real and enlarged (D) Virtual and enlarged
Ans: B (concave lens → always virtual, erect, diminished)
Q10. Splitting of white light into colours is called:
(A) Refraction (B) Dispersion (C) Reflection (D) Diffraction
Ans: B
(A) Refraction (B) Dispersion (C) Reflection (D) Diffraction
Ans: B
Q11. SI unit of power of a lens is:
(A) Metre (B) Dioptre (C) Watt (D) Joule
Ans: B
(A) Metre (B) Dioptre (C) Watt (D) Joule
Ans: B
Q12. Object at 2F of a convex lens. Image is at:
(A) F (B) 2F (C) Between F and 2F (D) Beyond 2F
Ans: B (image at 2F, same size, real, inverted)
(A) F (B) 2F (C) Between F and 2F (D) Beyond 2F
Ans: B (image at 2F, same size, real, inverted)
Q13. Critical angle for glass-air is about:
(A) 24° (B) 42° (C) 49° (D) 90°
Ans: B
(A) 24° (B) 42° (C) 49° (D) 90°
Ans: B
Q14. The lens formula is:
(A) 1/f = 1/u + 1/v (B) 1/f = 1/v − 1/u (C) 1/f = u + v (D) 1/f = 1/u − 1/v
Ans: B
(A) 1/f = 1/u + 1/v (B) 1/f = 1/v − 1/u (C) 1/f = u + v (D) 1/f = 1/u − 1/v
Ans: B
Q15. A convex lens (f = 20 cm) has object at 30 cm. Image position?
1/v = 1/20 + 1/(−30) = 1/20 − 1/30 = 1/60
Ans: v = +60 cm (real, inverted, enlarged, beyond 2F)
Q16. TIR requires light to go from:
(A) Rarer to denser (B) Denser to rarer, i > C (C) Denser to rarer, i < C (D) Any direction
Ans: B
(A) Rarer to denser (B) Denser to rarer, i > C (C) Denser to rarer, i < C (D) Any direction
Ans: B
Q17. The refractive index of a medium depends on:
(A) Wavelength of light (B) Nature of medium (C) Both A and B (D) Neither
Ans: C
(A) Wavelength of light (B) Nature of medium (C) Both A and B (D) Neither
Ans: C
Q18. Two thin lenses of power +2 D and −1 D are combined. Net power is:
Ans: P = +2 + (−1) = +1 D
Ans: P = +2 + (−1) = +1 D
16) Practice Problems — 18 Numericals with Step-by-Step Solutions
Problem 1: Light enters water (n = 1.33) from air at i = 60°. Find r.
1 × sin 60° = 1.33 × sin r
0.866 = 1.33 sin r
sin r = 0.866/1.33 = 0.651
r = sin⁻¹(0.651) = 40.6°
Problem 2: Find n if light bends from 50° to 30° when entering a medium.
n = sin i / sin r = sin 50° / sin 30° = 0.766 / 0.5 = 1.532
Problem 3: Speed of light in glass is 2 × 10⁸ m/s. Find n of glass.
n = c/v = 3 × 10⁸ / 2 × 10⁸ = 1.5
Problem 4: A pool appears 1.2 m deep. n = 1.33. Find actual depth.
Real depth = n × apparent depth = 1.33 × 1.2 = 1.6 m
Problem 5: Find the critical angle for water-air boundary (n = 1.33).
sin C = 1/n = 1/1.33 = 0.752
C = sin⁻¹(0.752) = 48.8° ≈ 49°
Problem 6: A convex lens of f = 25 cm has object at 40 cm. Find v, m, and nature.
f = +25 cm, u = −40 cm
1/v = 1/f + 1/u = 1/25 + 1/(−40) = 1/25 − 1/40 = (8−5)/200 = 3/200
v = +66.67 cm (real, beyond 2F)
m = v/u = 66.67/(−40) = −1.667 (real, inverted, enlarged)
Problem 7: A convex lens of f = 10 cm has object at 6 cm. Find v, m, nature.
u = −6 cm, f = +10 cm, u < f → virtual image
1/v = 1/10 + 1/(−6) = 1/10 − 1/6 = (3−5)/30 = −2/30 = −1/15
v = −15 cm (same side, virtual)
m = v/u = −15/(−6) = +2.5 (virtual, erect, enlarged)
Problem 8: A concave lens of f = −15 cm has object at 20 cm. Find v, m, nature.
u = −20 cm, f = −15 cm
1/v = 1/f + 1/u = 1/(−15) + 1/(−20) = −1/15 − 1/20 = (−4−3)/60 = −7/60
v = −8.57 cm (same side, virtual)
m = v/u = −8.57/(−20) = +0.429 (virtual, erect, diminished)
Problem 9: A convex lens produces a real image 3 times the size of object. If f = 12 cm, find u.
m = −3 (real → inverted → negative)
m = v/u = −3 → v = −3u
1/12 = 1/(−3u) − 1/u = −1/(3u) − 1/u = −1/(3u) − 3/(3u) = −4/(3u)
−4/(3u) = 1/12 → −48 = 3u → u = −16 cm
Problem 10: A lens has power −2 D. Find its focal length and type.
f = 1/P = 1/(−2) = −0.5 m = −50 cm
Negative focal length → concave lens
Problem 11: A convex lens of f = 15 cm produces a virtual image at 30 cm. Find u.
v = −30 cm (virtual → same side → negative)
1/u = 1/v − 1/f = 1/(−30) − 1/15 = −1/30 − 1/15 = −1/30 − 2/30 = −3/30 = −1/10
u = −10 cm (u < f, object between O and F)
Problem 12: Light enters a medium at 45° and refracts at 28°. Find n of the medium.
n = sin 45° / sin 28° = 0.7071 / 0.4695 = 1.506
Problem 13: A fish appears at 30 cm below water surface. n = 1.33. Actual depth?
Real depth = n × apparent = 1.33 × 30 = 39.9 cm ≈ 40 cm
Problem 14: Find the focal length of a lens of power +2.5 D.
f = 1/2.5 = 0.4 m = 40 cm (convex lens)
Problem 15: An object at 12 cm from a convex lens (f = 8 cm) gives a real image. Find magnification.
1/v = 1/8 + 1/(−12) = 1/8 − 1/12 = (3−2)/24 = 1/24
v = +24 cm
m = v/u = 24/(−12) = −2 (real, inverted, enlarged)
Problem 16: A convex lens (f = 5 cm) is used as a magnifying glass. Where should an object be placed to get 3× magnification?
m = +3 (virtual → erect → positive)
m = v/u = 3 → v = 3u
v is −ve (virtual, same side), so v = 3u (where u is −ve)
1/5 = 1/(3u) − 1/u = 1/(3u) − 3/(3u) = −2/(3u)
u = −10/3 = −3.33 cm
Problem 17: Two lenses of power +3 D and −2 D are in contact. Find net power and focal length.
P = +3 + (−2) = +1 D
f = 1/1 = 1 m = 100 cm (convex lens)
Problem 18: A coin at the bottom of a beaker of water (n = 1.33) appears at 6 cm depth. Find actual depth and apparent shift.
Actual depth = 1.33 × 6 = 7.98 cm ≈ 8 cm
Apparent shift = 8 − 6 = 2 cm
17) Common Mistakes ❌ — Don't Lose Marks!
❌ Mistake 1: Using mirror formula 1/f = 1/u + 1/v for lenses.
✅ Fix: Lens formula is 1/f = 1/v − 1/u. DIFFERENT from mirror formula!
✅ Fix: Lens formula is 1/f = 1/v − 1/u. DIFFERENT from mirror formula!
❌ Mistake 2: Using m = −v/u for lenses (that's for mirrors).
✅ Fix: For lenses: m = v/u (no negative sign). For mirrors: m = −v/u.
✅ Fix: For lenses: m = v/u (no negative sign). For mirrors: m = −v/u.
❌ Mistake 3: Sign of f for convex and concave lenses.
✅ Fix: Convex → f = +ve. Concave → f = −ve. (Opposite of mirrors!)
✅ Fix: Convex → f = +ve. Concave → f = −ve. (Opposite of mirrors!)
❌ Mistake 4: Confusing v sign — real vs virtual for lenses.
✅ Fix: For lenses: real image is on the opposite side → v = +ve. Virtual image is on the same side → v = −ve. (Opposite of mirrors!)
✅ Fix: For lenses: real image is on the opposite side → v = +ve. Virtual image is on the same side → v = −ve. (Opposite of mirrors!)
❌ Mistake 5: Forgetting to convert cm to m for power.
✅ Fix: P = 1/f where f is in metres. f = 50 cm → f = 0.5 m, P = +2 D.
✅ Fix: P = 1/f where f is in metres. f = 50 cm → f = 0.5 m, P = +2 D.
❌ Mistake 6: Thinking higher n means higher speed.
✅ Fix: Higher n → LOWER speed. n = c/v, so v = c/n. Higher n → more slowing.
✅ Fix: Higher n → LOWER speed. n = c/v, so v = c/n. Higher n → more slowing.
❌ Mistake 7: Confusing direction of bending.
✅ Fix: Rarer → Denser: bends TOWARD normal. Denser → Rarer: bends AWAY FROM normal. Think: "Light wants to be fast (in rarer) so it takes a straighter path away from the crowd (normal)."
✅ Fix: Rarer → Denser: bends TOWARD normal. Denser → Rarer: bends AWAY FROM normal. Think: "Light wants to be fast (in rarer) so it takes a straighter path away from the crowd (normal)."
❌ Mistake 8: Using cm in Snell's law or power formula.
✅ Fix: Snell's law uses ratios (no units). Power formula requires f in metres (not cm).
✅ Fix: Snell's law uses ratios (no units). Power formula requires f in metres (not cm).
18) Quick Revision — One-Liners
- Refraction: bending of light due to speed change at medium boundary.
- Rarer → denser: bends toward normal. Denser → rarer: bends away from normal.
- Snell's law: n₁ sin i = n₂ sin r. sin i / sin r = n₂₁ = constant.
- Refractive index: n = c/v. Unitless. n ≥ 1 always.
- n_water = 1.33, n_glass ≈ 1.5, n_diamond = 2.42.
- Higher n → slower light → more bending.
- Reversibility: n₁₂ = 1/n₂₁.
- Glass slab: emergent ray parallel to incident ray (lateral shift).
- Apparent depth = Real depth / n. Pool looks shallower.
- TIR: denser → rarer, i > C. sin C = 1/n.
- TIR applications: optical fibre, diamond sparkle, mirage, endoscopy.
- Convex lens (converging): f > 0. Concave lens (diverging): f < 0.
- Lens formula: 1/f = 1/v − 1/u. Magnification: m = v/u.
- Convex lens: object between O and F → virtual, erect, enlarged (magnifying glass).
- Concave lens: ALWAYS virtual, erect, diminished.
- Power P = 1/f(m). Unit: dioptre (D). Convex → +ve, Concave → −ve.
- Combination: P_total = P₁ + P₂ + ...
- Dispersion: white light → VIBGYOR. Violet deviates most.
- Rainbow: refraction + dispersion + TIR in water droplets. Primary at 42°.
- Critical angles: water 49°, glass 42°, diamond 24°.
✅ Refraction of Light — Fully Covered! Complete reference with Snell's law, refractive index, real/apparent depth, TIR, lens formula, power, dispersion, 18 PYQs, 18 solved numericals, 8 common mistakes, and quick revision. Focus on lens formula and sign convention for AMU success! 💡🔥