What must be the index of refraction of the liquid such that the direction of the light entering the liquid is not changed?

A ray of light is travelling in glass and strikes a glass/liquid interface. The angle of incidence is 51.0°, and the index of refraction of glass is n = 1.50.

1 Answer
A08
Apr 20, 2016

The refractive index of liquid must be #=1.50#

Explanation:

If a ray of light is traveling from glass to liquid, we know that

#sin\theta_l = \frac{n_g}{n_l}\sin\theta_g# ......(1)

where #theta_l and theta_g# are angel of refraction and angle of incidence and #n_l and n_g# are respective refractive indices.

It is required that the direction of light entering liquid must not change. This implies that #theta_l = theta_g#. If we insert this equality in the expression (1), we obtain

#n_l = n_g=1.50#
This is independent of angle of incidence.

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