Question

A ray of light deviates 15° away from normal on going from one medium to another
medium. If angle of refraction is 45°, then show that refractive index of second medium with
respect to first medium is
$\frac{1}{\sqrt{2} }$

​

Answer 1

Given : A ray of light deviates 15° away from normal on going from one medium to another medium. angle of refraction is 45°

To show : refractive index of 2nd medium with respect to first medium is 1/√2

solution : angle of refraction, r = 45°

angle of incidence, i = 45° - deviation angle = 45° - 15° = 30°

now using Snell's law,

μ₁sini = μ₂sinr

⇒μ₁ × sin30° = μ₂ × sin45°

⇒μ₁ × 1/2 = μ₂ × 1/√2

⇒μ₁/√2 = μ₂

⇒μ₂/μ₁ = 1/√2

Therefore the refractive index of 2nd medium with respect to 1st medium is 1/√2.

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