A plastic hemisphere has a radius of curvature of 8cm and an index of refraction of 1.6. On the axis halfway between the plane surface and the spherical one (4cm 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.

Options

A. 1.0cm
B. 1.5cm
C. 3.75cm
D. 2.5cm

Answer

d.

Explanation

Distance of image from the plane surface is as follows:
`x_(1)=(4)/(1.6)`
`=2.5cm(d_(app)=(d_(actual))/(mu))`
For the curved side
`(1.6)/(4)+(1)/(x_(1))=(1-1.6)/(8)`
`:. x_(2)~~-3.0cm`
The minus sign means the image is on the object side.
`:. I_(1)I_(2)=(8-2.5-3.0)cm=2.5cm`