Question

The diagram shows a spherical surface which separates two media of refractive indices, ${\mu }_1$ and ${\mu }_2$ , respectively. Now, a point object is placed on the principal axis as shown in the figure. Then

• A. Real image will form if ${\mu }_1>{\mu }_2$ and for all values of $u$
• B. Real image for some values of $u$ if ${\mu }_1>{\mu }_2$
• C. Virtual image will form if ${\mu }_1>{\mu }_2$
• D. Virtual image will form if ${\mu }_1<{\mu }_2$

Answer 1

Answer: (C)

$\frac{{\mu }_2}{v}-\frac{{\mu }_1}{-u}=\frac{{\mu }_2-{\mu }_1}{R}$
$\Rightarrow v=\frac{uR{\mu }_2}{u\left({\mu }_2-{\mu }_1\right)-R{\mu }_1}$
$\Rightarrow v=\frac{uR{\mu }_2}{u{\mu }_2-{\mu }_1(u+R)}$
We can see that ${\mu }_1>{\mu }_2$ then image distance is negative which means virtual image