A vessel, whose bottom is flat and perfectly reflecting, is filled with water ( index = 4/3 ) upto a height = 40 cm . A point object in air above is moving towards the water surface with a constant sp

Question

A vessel, whose bottom is flat and perfectly reflecting, is filled with water ( index = 4/3 ) upto a height = 40 cm . A point object in air above is moving towards the water surface with a constant speed = 4 m/s. What is the relative speed of its final image (in m/s), as seen by the object itself, at a moment when the object is 30 cm above the water surface ?

TestHub · Accepted Answer

An object at height x above the water surface appears, from inside water, at μx above it. The reflecting bottom is at real depth h = 40 cm.

The mirror forms the image at (μx + h) behind it; converting the total depth back for an observer in air, the final image appears at a depth $x + \frac{2 h}{μ} = x + 2 \times 40 \times \frac{3}{4} = x + 60 cm$ below the surface.

Separation between object and image = 2x + 60 cm, and it changes at

$\frac{d}{d t} (2 x + 60) = 2 \times 4 = 8 m/s$

Answer: 8

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