Question

A glass hemisphere of radius 10 cm is placed in air. A point object P is placed at distance 10 cm from curved surface.

• A. Final image is real
• B. Final image is virtual
• C. Final image is at $\frac{180}{3}cm$ before the plane surface
• D. None of the above

Answer 1

The correct option is B Final image is virtual

$\text{Refraction at curved surface.}$

$\begin{array}{c}\frac{{\mu }_1}{f}=\frac{{\mu }_2}{u}=\frac{{\mu }_1-{\mu }_2}{R}\\ \frac{3}{2v}-\frac{1}{-10}=\frac{\frac{3}{2}-1}{10}\\ \frac{3}{2v}=\frac{1}{20}-\frac{1}{10}\\ \frac{2v}{3}=-20\\ v=-30\end{array}$

The distance of intermediate image

from plane surface. $=10+30=40cm$

$\begin{array}{c}\frac{AD}{RD}=\frac{{\mu }_1}{{\mu }_2}\\ AD=\frac{40}{\frac{3}{2}}=-\frac{80}{3}\text{before plane surface}\\ \text{since object and image are some side of}\\ \text{refracting hemisphere image is virtual.}\end{array}$

Option B is correct