Question

The optical path of a ray of light of a given wavelength travelling a distance of 3 cm in flint glass having refractive index 1.6 is same as that on travelling a distance x cm through a medium having refractive index 1.25. Determine the value of x.

Answer 1

Let d_fg and d_m be the distances by the ray of light in the flint glass and the medium respectively. Also, let n_fg and n_m be the refractive indices of the flint glass and the medium respectively.

Given : d_fg = 3 cm, n_fg = 1.6, n_m = 1.25,

Optical path = n_m x d_m = n_fg x d_fg

∴ d_m = \(\frac{n_{fg}×d_{fg}}{n_m}\) = 3.84 cm

Thus, x cm = 3.84 cm

∴ x = 3.84

This is the value of x.