Optics Question 799

Question: 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:

Options:

A) 14 cm below flat surface

B) 20 cm below flat surface

C) 16 cm below flat surface

D) 30 cm below flat surface

Show Answer

Answer:

Correct Answer: B

Solution:

[b] Given, radius of hemispherical glass R=10cm

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

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

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=20cm. $

Apparent height, $ h _{a}=h _{r}\frac{{\mu _{1}}}{{\mu _{2}}}=30\times \frac{1}{1.5}=20cm $ below flat surface.



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