A small source of light is mounted inside a cylindrical container of height h . The bottom of the container is covered with a mirror. Initially, the container is empty. Then a clear liquid with the in

Question

A small source of light is mounted inside a cylindrical container of height $h$ . The bottom of the container is covered with a mirror. Initially, the container is empty. Then a clear liquid with the index of refraction $n$ is slowly poured into the container. The level of liquid H rises steadily, reaching the top of the container in time T . Let $h_{1}$ be the distance of source of the light from the bottom of the container. Consider paraxial ray approximation.

Consider two cases

1) H ≤ h₁2) h₁ ≤ H ≤ h

TestHub · Accepted Answer

Case (1) v I ​ = ( 1 − μ i ​ μ r ​ ​ ) v R ​ + μ i ​ μ r ​ ​ v 0 ​ H = T h ​ t v R ​ = dt dH ​ = T h ​ Velocity of image after first refraction v I ​ = ( 1 − n ) ( T h ​ ) j ^ ​ Velocity of image after reflection in mirror V I ′ ​ = ( 1 − n ) ( T h ​ ) ( − j ^ ​ ) Velocity of image after second refraction V I = ( 1 − n 1 ​ ) ( T h ​ ) j ^ ​ + n 1 ​ ( 1 − n ) ( T h ​ ) ( − j ^ ​ ) V I = 2 ( 1 − n 1 ​ ) T h ​ j ^ ​ Case (2) v I ​ = ( 1 − n 1 ​ ) T h ​ j ^ ​

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JEE Main + Advanced (1 year 12th class)

JEE Advanced (2028)