As shown in the figure, a plane mirror is fixed at a height of 50 cm from the bottom of tank containing water (μ=4/3). The height of water in the tank is 8 cm. A small bulb is placed at the bottom of the water tank. The distance of image of the bulb formed by mirror from the bottom of the tank is ___________ cm.

Solution

Physics sir · 4 steps

First let the water lift the bulb, then let the mirror reflect that raised bulb.

1. Water lifts the bulb. Light from the bulb leaves the water before it reaches the mirror. Seen from above the water, the bulb appears at depth 8/(4/3) = 6 cm below the surface.

   shift = t(1 - 1/μ) = 8(1 - 3/4) = 2 cm

2. Object for the mirror. The mirror therefore sees the bulb 2 cm above the bottom. That point is 50 - 2 = 48 cm below the mirror.
3. Mirror image. A plane mirror forms the image as far behind it as the object is in front. So the image is 48 cm above the mirror.
4. So. Measured from the bottom of the tank, the image is at 50 + 48 = 98 cm.

The common slip: 100. Ignoring the water and treating the bulb as 50 cm below the mirror gives 100, not 98.

The idea to keep. When a slab or liquid sits between an object and a mirror, first find where the object appears after refraction. The mirror reflects that apparent position, not the real one.

Answer from the NTA final answer key. Solution by PrepWiser.