Question

A glass hemisphere of radius $R$ and of material having refractive index $1.5$ is silvered on its flat face as shown in figure. A small object of height $h$ is located at a distance at a distance $2R$ from the surface of hemisphere as shown in figure. The final image will not form

• A. At a distance of $R$ from silvered surface, on the right side
• B. On the object itself
• C. At hemisphere surface
• D. left side of the object and of same size of the object.

Answer 1

Answer: (A), (C), (D)

left side of the object and of same size of the object.

Here, three optical phenomena take place-first refraction, then reflection and finally refraction.

For 1st refraction, $\frac{15}{v}-\frac{1}{-2R}=\frac{1.5-1}{R}$

$\frac{1.5}{v}=0\Rightarrow v\to \infty$

i.e. rays after refraction get parallel to the axis and strike the mirror normally, get reflected and retraced back , and final image is formed at the same placed where the object is and of same size(i.e., auto collimation).
Hence, the image would be real.


Hence, only option $A,C,D$ are correct.