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 form.

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

Answer 1

The correct option is B On the object itself

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 retracted 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 $B$ is correct.