Refraction and Lenses
~10 min read
- Refraction: Bending of light at the boundary of two media. Snell's law: n₁sin i = n₂sin r.
- Lenses: Convex (converging) and concave (diverging). Lens formula 1/v - 1/u = 1/f. Power P = 1/f (in metres). Unit: dioptre.
- Total internal reflection: Occurs when light travels from denser to rarer medium at angle > critical angle. Used in optical fibres, prisms, diamonds.
Refraction is the bending of light when it changes media. Lenses use refraction to form images. NDA tests Snell's law, lens formula, total internal reflection, and applications.
Snell's Law
n₁ sin θ₁ = n₂ sin θ₂
- n = refractive index. Light bends when speed changes between media.
- n = c/v (speed of light in vacuum / speed in medium).
- Common refractive indices: Air ≈ 1.0003, Water = 1.33, Glass = 1.5, Diamond = 2.42.
- Light bending: From rarer (low n) to denser (high n) — bends toward normal. From denser to rarer — bends away from normal.
Total Internal Reflection (TIR)
- Occurs when light goes from denser to rarer medium AND angle of incidence > critical angle.
- Critical angle: The angle of incidence (in denser medium) at which the refracted ray skims along the boundary. sin θ_c = n_rarer/n_denser.
- For water-air: θ_c ≈ 48.6°. For glass-air: θ_c ≈ 42°. For diamond-air: θ_c ≈ 24.4°.
- Applications:
- Optical fibres (light travels long distances by repeated TIR).
- Prisms (binoculars, periscopes — 90° prisms).
- Diamond brilliance (high refractive index = small critical angle = lots of TIR).
- Mirage (hot road appears wet due to TIR in heated air layers).
Lenses
- Convex (converging) lens: Thicker in middle. Converges parallel rays to focus.
- Concave (diverging) lens: Thinner in middle. Diverges parallel rays — they appear to come from focus.
- Focal length (f): Distance from lens to focus.
- Power (P): P = 1/f (in metres). SI unit: dioptre (D).
- Positive P: convex lens. Negative P: concave lens.
Lens Formula and Magnification
Lens formula: 1/v - 1/u = 1/f
Magnification: m = h'/h = v/u
Sign convention (Cartesian):
- Object on left side. Light travels left to right (+ve direction).
- Object distance u is -ve (left of lens, against light).
- For convex lens: f is +ve. For concave: f is -ve.
- Real image: v > 0. Virtual image: v < 0.
Image Formation by Convex Lens
| Object Position | Image |
|---|---|
| At infinity | At F. Real, inverted, point-sized |
| Beyond 2F | Between F and 2F. Real, inverted, diminished |
| At 2F | At 2F on other side. Real, inverted, same size |
| Between F and 2F | Beyond 2F. Real, inverted, enlarged. Used in: camera (object far), projector |
| At F | At infinity. Highly enlarged |
| Between lens and F | Same side as object. Virtual, erect, enlarged. Used in: simple microscope, magnifying glass |
NDA PYQ Examples
Q: Which optical principle is used in optical fibres?
(a) Refraction (b) Reflection (c) Total internal reflection (d) Diffraction
Answer: (c) Total internal reflection.
Q: The SI unit of power of a lens is:
(a) Watt (b) Newton (c) Dioptre (d) Lux
Answer: (c) Dioptre = 1/m (focal length in metres).
Q: A convex lens of focal length 25 cm has power:
(a) 0.25 D (b) 2.5 D (c) 4 D (d) 25 D
Answer: (c) 4 D. P = 1/f(m) = 1/0.25 = 4 D.
Q: Refractive index of diamond is approximately:
(a) 1.0 (b) 1.33 (c) 1.5 (d) 2.42
Answer: (d) 2.42 — highest of common materials.
Drill Refraction and Lenses for NDA
NDA-pattern items on Refraction and Lenses with answer keys and explanations.
Start Free Mock TestFrequently Asked Questions
Why does a coin in a glass of water appear closer to the surface?
Refraction. Light from the coin bends as it passes from water (n = 1.33) to air (n = 1) — it bends away from the normal. Our eyes trace the bent ray back in straight lines, so the coin appears at a shallower position.
Why do diamonds sparkle?
High refractive index (n = 2.42) gives diamond a small critical angle (~24°). Most light entering the diamond undergoes total internal reflection multiple times before exiting. The cut also disperses light into colours.
How does an optical fibre transmit signals?
Light enters the fibre's core. The cladding has a lower refractive index than the core, so light bouncing within the core stays trapped by total internal reflection. Signals travel for kilometres with minimal loss.
Why is sky blue?
Rayleigh scattering. Sunlight contains all colours; air molecules scatter shorter wavelengths (blue, violet) more than longer (red). Our eyes are more sensitive to blue than violet, so we see blue sky. (Covered in Dispersion topic page.)
What does dioptre mean?
Unit of optical power. 1 dioptre = power of a lens with 1 metre focal length. Spectacles for short sight (myopia) might have -2 D; for far sight, +1.5 D. The bigger the number, the stronger the lens.