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Question

One face of a rectangular glass plate of thickness 6 cm is silvered. an object is placed at a distance of 8 cm in front of the unsilvered face. Its image is formed 10 cm behind the silvered face. The refractive index of glass plate is :
  1. 53
  2. 43
  3. 76
  4. 32

A
43
B
53
C
32
D
76
Solution
Verified by Toppr

Let the refractive index of medium be η. The thickness of glass slab is 6xcm. But due to refraction, the appeared thickness would be different (<6xcm) as η>1.

So the appeared distance of object from the silvered face (which acts as a plane mirror) would be (8+x)xcm.

Also the appeared distance of the image from silvered surface would be (6x+10)xcm=(16x)xcm.

By law of reflection from plane mirror, distance of the object from mirror is equal to the distance of image from the mirror.
Thus, 8+x=16x.

Solving the equation above, we get, x=4xcm.

As, η=Distance in vacuum airDistance in material=64=1.5

So the refractive index of the glass is equal to 1.5

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