A hemispherical portion of the surface of a solid glass sphere (mu = 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 centre 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.

Answer

0

Explanation

Let the object be placed at `A`
Then for refraction at the unsilvered part `u=-2r,R=r` .
`tharefore (mu_(2))/(v)-(mu_(1))/(u)=(mu_(2)-mu_(1))/(R)`
`=(3//2)/(v) -(1)/((-2r))=(3/2-1)/(r) rArrv=infty`
so, image formed at infinity will act as an object for the silvered part and hence the image will be formed at the foucs of thhe concave mirror `i.e.,` at `(r)/(2)` distance left ward from `D`
Again for refraction at the unsilvered surface `u=(r+(r)/(2))=(3r)/(2)`
`therefore (1)/(v)-(3/2)/((3r)/(2))=(1-3/2)/(r)` or `v=2r`. Hence the final formed at `D`