Question

A point object is placed at distance x from a transparent hemisphere of refractive index $\mu =\frac{3}{2}$. For what value of x we will not get real image?

• A. $\frac{3}{2}R$
• B. $\frac{5}{2}R$
• C. 3R
• D. 5R

Answer 1

The correct option is A $\frac{3}{2}R$

$\frac{{\mu }_2}{v}-\frac{{\mu }_1}{u}=\frac{{\mu }_2-{\mu }_1}{R}\Rightarrow \frac{3}{2v}+\frac{1}{x}=\frac{\frac{3}{2}-1}{R}\frac{3}{2v}=\frac{1}{2R}-\frac{1}{x}$

For the image to be virtual, the condition on $v$ is, $v<0$.
$\Rightarrow x<2R$