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.

Answer 1

The refractive index of liquid must be #=1.50#

We can determine that if a light beam passes through glass and into a liquid

#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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Answer 2

Carson Alexander

The index of refraction of the liquid must be equal to the index of refraction of the medium from which the light enters.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.