Refraction and Total Internal Reflection
~9 min read
- Refraction: Bending of light at interface of two media. Snell's law: n₁ sin i = n₂ sin r.
- Refractive index: n = c/v. Higher n means slower light in that medium.
- TIR: Occurs when light goes from denser to rarer at angle > critical angle. Used in optical fibres, prisms, mirage.
Light slows down and bends when it enters a new medium. CDS/OTA tests Snell's law, refractive index, critical angle and applications like optical fibres, mirages and sparkle of diamond.
Refraction and Snell's Law
- Bending of light at the boundary of two transparent media.
- Cause — light travels at different speeds in different media.
- Snell's law: n₁ sin i = n₂ sin r.
- Light bends towards normal when going from rarer to denser medium (air to water).
- Light bends away from normal when going from denser to rarer (water to air).
- Frequency does not change in refraction; wavelength and speed do.
Refractive Index
| Medium | Refractive index (n) |
|---|---|
| Vacuum | 1.000 (exact) |
| Air | 1.0003 (taken as 1) |
| Water | 1.33 |
| Glass (crown) | 1.50 |
| Glass (flint) | 1.65 |
| Diamond | 2.42 |
n = speed of light in vacuum / speed in medium = c/v.
Total Internal Reflection
- Occurs when light travels from denser to rarer medium at an angle of incidence greater than the critical angle.
- Critical angle θ_c: sin θ_c = 1/n.
- For water (n=1.33), θ_c ≈ 48.6°. For glass (n=1.5), θ_c ≈ 41.8°. For diamond (n=2.42), θ_c ≈ 24.4° — explains its sparkle.
- Applications: Optical fibres (telecom, endoscopy), totally reflecting prisms (binoculars, periscope), mirage, sparkle of diamond.
Everyday Refraction Phenomena
- Pencil in water appears bent.
- Apparent depth of pool is less than real depth (n_water = 1.33, depth/n ≈ 0.75×).
- Twinkling of stars — due to refraction by varying atmospheric layers.
- Mirage in deserts — hot air near ground is rarer; TIR makes sky appear as water.
- Apparent sunrise / sunset — Sun is visible ~2 minutes before actual sunrise and after sunset due to atmospheric refraction.
CDS/OTA PYQ Examples
Q: A mirage in a desert is caused by:
(a) Reflection from sand (b) Refraction and total internal reflection (c) Dispersion (d) Diffraction
Answer: (b) Refraction and TIR through hot air layers.
Q: Refractive index of diamond is approximately:
(a) 1.33 (b) 1.50 (c) 2.42 (d) 3.50
Answer: (c) 2.42 — highest among common substances; gives diamond its sparkle.
Q: Optical fibres work on the principle of:
(a) Reflection (b) Refraction (c) Total internal reflection (d) Diffraction
Answer: (c) Total internal reflection — signal stays trapped inside the fibre.
Q: When light passes from air to water, its:
(a) Frequency decreases (b) Wavelength decreases (c) Speed increases (d) Energy changes
Answer: (b) Wavelength decreases; speed also decreases; frequency unchanged.
Q: Sun is visible before actual sunrise and after sunset because of:
(a) Reflection (b) Refraction (c) Dispersion (d) Diffraction
Answer: (b) Atmospheric refraction.
Drill Refraction and Total Internal Reflection for CDS/OTA
CDS/OTA-pattern items on Refraction and Total Internal Reflection with answer keys and explanations.
Start Free Mock TestFrequently Asked Questions
Why does a pencil in water appear bent?
Light from the submerged part is refracted as it leaves water, so our eye traces it back along a straight line to a shifted apparent position.
Why do stars twinkle but planets do not?
Stars are point sources — atmospheric refraction varies, making their light flicker. Planets are extended disks; the averaging across the disk removes flicker.
How does an optical fibre work?
A glass/silica core surrounded by lower-index cladding traps light through repeated total internal reflections. Used in high-speed internet, cable TV, and medical endoscopes.