A cubic container is filled with a liquid whose refractive index increases linearly from top to bottom. Which of the following graphs correctly represent the path of a ray of light inside the liquid?

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Solution

We know that, when a ray of light passes from rarer to denser medium, it bends towards the normal and when the light ray passes from denser to rarer medium, it bends away from the normal.

Since the refractive index is changing, the light cannot travel in a straight line in the liquid as shown in options (c) and (d).

Hence, options (c) and (d) are the wrong answers.

For a cubical container filled with liquid, While the light ray moves from top to bottom, it bends towards the normal, as the refractive index increases linearly from top to bottom and upon reflection at the bottom, while it moves from bottom to top, it bends away from the normal as the refractive index decreases linearly.

Initially, it will bend towards normal and after reflecting from the bottom it will bend away from the normal as shown in schematic representation below.

Hence, option (a) is the correct answer.

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