Question

A glass hemisphere $\left(\mu = \text{1.5}\right)$ has a radius of curvature of $16cm$ . A small object $O$ is located on its axis halfway between the plane and spherical surface. The distance between two images, when viewed along the axis from the sides of the hemisphere, is

• A. $\frac{32}{15} \, \text{cm}$
• B. $\frac{48}{15} \, \text{cm}$
• C. $\frac{64}{15} \, \text{cm}$
• D. $\frac{80}{15} \, \text{cm}$

Answer 1

Answer: (C)

When viewed from spherical side,
$\frac{1}{v_{1}}+\frac{3}{2 \times 8}=\frac{1}{2 \times 16}$
$\Rightarrow \, \frac{1}{v_{1}}=\frac{1}{32}-\frac{3}{16}=\frac{- 5}{32}$
Image position is $\frac{32}{5}cm$ inside the hemisphere from its periphery.
And when viewed from plane side then image is at $\frac{16}{3}cm$ inside the plane surface.
$\therefore \, Δx=16-\frac{16}{3}-\frac{32}{5}=\frac{64}{15}cm$