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Q.

A hemispherical glass body of radius 10cm and refractive index 1.5 is silvered on its curved surface. A small air bubble is 6cm below the flat surface inside it along the axis. The position of the image of the air bubble made by the mirror is seen:

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a

14 cm below flat surface

b

16 cm below flat surface

c

20 cm below flat surface

d

30 cm below flat surface

answer is B.

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Detailed Solution

Given, radius of hemisphere glass R=10cm
$∴$ Focal length $f = \frac{10}{2} = - 5 c m$
$u = (10 - 6) = - 4 c m$
By using mirror formula
$\frac{1}{v} + \frac{1}{u} = \frac{1}{f} \Rightarrow \frac{1}{v} + \frac{1}{- 4} = \frac{1}{- 5} \Rightarrow v = 20 c m$
Apparent height, $h_{a} = h_{r} \frac{μ_{1}}{μ_{2}} = 30 \times \frac{1}{1.5}$ =20cm
Below flat surface

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