Refractive Index - UNSOLVED PRACTICE SET

Q7. Define refractive index. Write two equivalent formulas for it (one using speed of light, one using Snell's Law angles).

Q8. The speed of light in water is 2.25 × 10⁸ m/s. Speed in vacuum = 3 × 10⁸ m/s. Calculate the refractive index of water.

Q9. Diamond has a very high refractive index (n = 2.42). What does this tell us about:
(a) the speed of light in diamond, and 

(b) how much light bends when entering diamond from air?

Q10. Explain optical density. How is optical density related to refractive index? Is optically denser the same as physically/mass denser? Give an example where they differ.

Q11. Glass has n = 1.5. Find the speed of light in glass. (c = 3 × 10⁸ m/s) Also find the wavelength of yellow light (vacuum wavelength = 600 nm) inside the glass.

Q12. Explain why the refractive index of a medium for light depends on the colour (frequency) of the light. Give an example of a phenomenon this causes.

Q13. Explain the concept of refractive index in detail. Your answer must include:
(a) definition as n = c/v,
(b) the physical meaning — what it tells us about the optical density of the medium,
(c) how refractive index connects to Snell's Law: n₁ sin θ₁ = n₂ sin θ₂,
(d) a table of refractive indices for air, water, glass, and diamond with their approximate speeds of light,
(e) why diamond sparkles (connect to very high n and total internal reflection).

Q14. Optical fibres, used in internet cables and endoscopes in hospitals, work on the principle of total internal reflection which is related to refractive index.
(a) Define critical angle and total internal reflection.
(b) Show using Snell's Law that sin C = n₂/n₁ when the refracted angle = 90°.
(c) Why must the light inside the fibre travel at angles greater than the critical angle? 

(d) The refractive index of the glass core of an optical fibre is 1.5 and cladding n = 1.0 (air). Find the critical angle.
(e) Name two applications of optical fibres in India.

Q15. Compare the refractive indices of different media and analyse the following:
(a) Light travels from glass (n = 1.5) to water (n = 1.33). Using ₁n₂ = n₂/n₁, find the relative refractive index.
(b) Does light speed up or slow down going from glass to water?
(c) Does the light bend toward or away from the normal?
(d) For the reverse journey (water to glass), what is ₁n₂?
(e) Show that ₁n₂ × ₂n₁ = 1 using the values above.

Q16. The speed of light in a medium X is 1.8 × 10⁸ m/s. (c = 3 × 10⁸ m/s.)
(a) Calculate the refractive index of medium X.
(b) A ray of light hits medium X from air at 45° (sin 45° = 0.707). Using Snell's Law, find the angle of refraction.
(c) Find the wavelength of red light (vacuum λ = 700 nm) in medium X

Q17. The refractive indices of glass and water are 1.5 and 1.33 respectively.
(a) Find the speed of light in each medium.
(b) Find the critical angle for a glass-water interface (sin C = n_water/n_glass).
(c) A ray in glass hits the glass-water boundary at 60°. Is this beyond the critical angle? What happens? (sin of critical angle ≈ 0.887)

Q18. A light ray goes through three media in order: air (n₁=1) → glass (n₂=1.5) → water (n₃=1.33). At the first boundary, the angle in air is 50°.
(a) Find the angle in glass using Snell's Law.
(b) The same ray enters water from glass. Using Snell's Law again, find the angle in water.
(c) Compare the angle in water with the angle in air (50°). What do you observe?
(d) State the general rule: when light re-enters the first medium after passing through any number of parallel media, what is its angle? (sin 50° ≈ 0.766)