Question

A small object is placed 20 cm in front of a block of glass 10 cm thick and its farther side silvered.The image is formed 22 cm behind the silvered face.Find the refractive index of glass.
Options are
(a) 1.15
(b) 1.25
(c) 1.67
(d) 1.1

Answer 1

Answer on Question #50100, Physics, Optics

A small object is placed $20~\mathrm{cm}$ in front of a block of glass $10~\mathrm{cm}$ thick and its farther side silvered. The image is formed $22~\mathrm{cm}$ behind the silvered face. Find the refractive index of glass.

Options are

(a) 1.15

(b) 1.25

(c) 1.67

(d) 1.1

Solution:

The situation is shown in the figure. ABCD is the glass block, O is the object and I is the image. To an observer in front of the face AD, the silvered face BC appears to be shifted to a new position B'C' due to refraction at AD. B'C' act as a plane mirror in which the image I is formed.

Let $\mathsf{AB}^{\prime} = \mathsf{x}$ . Then, since for a plane mirror the image distance is equal to the object distance from the mirror, we have

$$2 0 + x = 2 2 + 1 0 - x$$ $$x = 6 \mathrm {c m}$$

Refractive index $= \frac{\text{Real depth}}{\text{Apparent depth}} = \frac{10}{6} = 1.67$

Answer: (c) 1.67

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