Question

A glass hemisphere of radius $R$ and material having refractive index $1.5$ is silvered on its flat face as shown in the figure. A small object of height $h$ is located at a distance $2R$ from the surface of the hemisphere. The final image will be

• A. on the hemispherical surface.
• B. inside the hemisphere.
• C. at a distance of $2R$ from the silvered surface on the left side.
• D. at a distance of $3R$ from the silvered surface on the left side.

Answer 1

The correct option is D at a distance of $3R$ from the silvered surface on the left side.

Given,

$u=-2R;{\mu }_2=1.5;{\mu }_1=1$

Refraction through a curved surface is,

$\frac{{\mu }_2}{v}-\frac{{\mu }_1}{u}=\frac{{\mu }_2-{\mu }_1}{R}$

$\Rightarrow \frac{1.5}{v}+\frac{1}{2R}=\frac{1.5-1}{R}$

$\Rightarrow \frac{1.5}{v}=\frac{0.5}{R}-\frac{1}{2R}=\frac{0.5}{R}-\frac{0.5}{R}=0$

$\therefore v=\infty$

As the rays after refraction get parallel to axis and strike the plane mirror normally, get retraced back, and the final image is formed at the same place where the object is and of the same size. Image would be real.

<!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> Hence, $\left(D\right)$ is the correct answer.