# A hemispherical glass body of radius 10 cm and refractive index 1.5 is silvered on its curved surface.  A small air bubble is 6 cm below the flat surface inside it along the axis.  The position of the image of the air bubble made by the mirror is seen : Option 1) 14 cm below flat surface Option 2) 30 cm below flat surface Option 3) 20 cm below flat surface Option 4) 16 cm below flat surface

As we learnt in

Relation between focal length and radius of curvature -

$f=\frac{R}{2}$

- wherein

This is valid only for smaller angle of incidence.

i.e.paraxial rays

Mirror Formula -

$\frac{1}{v}+\frac{1}{u}=\frac{1}{f}$

- wherein

$u=$ Object distance from pole of mirror.

$v=$ Image distance from pole of mirror.

$f=$ focal length of the mirror.

Relation between real depth and apparent depth -

$\frac{n_{i}}{d}= \frac{n_{r}}{d{}'}$

- wherein

$n_{i}$ = Refractive index of medium of incident.

$n_{r}$ = Refractive index of medium of refraction.

d = distance of object.

$d{}'$ = apparent  depth

Given radius of hemispherical glass R = 10 cm

$\therefore$   focla length $f=\frac{10}{2}=-5\ cm$

$u=(10-6)=-4\ cm$

By using mirror formula

$\frac{1}{v}+\frac{1}{u}=\frac{1}{f}=\frac{1}{v}+\frac{1}{-4}=\frac{1}{-5}\ \; \Rightarrow\ \; v = 20\ cm$

Apparent height $h_{a}=h_{r}\frac{\mu_{1}}{\mu_{2}}=30\times \frac{1}{1.5}=20\ cm$

below flat surface.

Correct option is 3.

Option 1)

14 cm below flat surface

This is an incorrect option.

Option 2)

30 cm below flat surface

This is an incorrect option.

Option 3)

20 cm below flat surface

This is the correct option.

Option 4)

16 cm below flat surface

This is an incorrect option.

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