Question

The thickness of quarter-wave plate made from a doubly refracting crystal is  6.7 x 10^-5 cm  for a light of wavelength  4800 Å . What is the corresponding thickness of half-wave plate for a light of wavelength  6000 Å ?

(a)  16.75 x 10^-5 cm

(b)  13.4  x 10^-5 cm

(c)  10.72 x 10^-5 cm

(d)  8.34 x 10^-5 cm

Answer 1

Correct option  (a)  16.75 x 10^-5 cm

Explanation:

If  n_e and n₀ are refractive indices of extraordinary and ordinary rays in case of doubly refraction then thickness of wave plate are given as (n_e -  n₀) = (in term of wavelength)

For half wavelength t₁ = λ/2  ...(i)

For quarter wavelength t₂ = λ/4  ...(ii)

By equation (i) and (ii) half wave plate  = 2× thickness of quarter wave plate