A hemispherical portion of the surface of a solid glass sphere (μ = 1.5) of radius r is silvered to make the inner side reflecting. An object is placed on the axis of the hemisphere at a distance 3r from the center of the sphere. The light from the object is refracted at the unsilvered part, then reflected from the silvered part and again refracted at the unsilvered part. Locate the final image formed.

As shown in the figure, OQ= 3r, OP= r and PQ=2r


For Refraction at BPA

By lens equation

(because u =-2r)

For the reflection in concave mirror


So, v= focal length of the mirror =

For the refraction of BPA of the reflected image

Here, u=

Negative sign indicates that the image ids produced inside BPA, Image should be at C.

Final image is formed at the reflecting surface of the sphere.