question_answer

A plastic hemisphere has a radius of curvature   of 8 cm and an index of refraction of 1.6. On the axis halfway between the plane surface and the spherical one (4 cm from each) is a small object O. The distance between the two images when viewed along the axis from the two sides of the hemisphere is approximately

A) 1.0 cm

B) 1.5 cm

C) 3.75 cm

D) 2.5 cm

Correct Answer: D

Solution :

[d]

Distance of image from the plane surface is

\[{{x}_{1}}=\frac{4}{1.6}=2.5cm\left( {{d}_{app}}=\frac{{{d}_{actual}}}{\mu } \right)\]

For the curved side, \[\frac{1}{{{x}^{2}}}-\frac{1.6}{4}=\frac{1-1.6}{8}\]

\[\therefore \]      \[{{x}_{2}}\approx -3.0cm\]

The minus sign means the image is on the object side

\[\therefore \]      \[{{l}_{1}}{{l}_{2}}=(8-2.5-3.0)cm=2.5cm\]