Question

An object is placed in front of a sphere of radius $R$ at a distance $x$ from the first surface. The value of $x$ for which the light after refraction from the first surface becomes parallel to the axis is

• A. $\frac{R}{(\mu-1)}$
• B. $\frac{R}{\mu+1}$
• C. $\frac{2 R}{(1+\mu)}$
• D. $\frac{R \mu}{(\mu+1)}$

Answer 1

Answer: (A)

Applying, Lens' maker formula, we get
$\frac{\mu_{2}}{v}-\frac{\mu_{1}}{u}=\frac{\mu_{2}-\mu_{1}}{R}$

$\Rightarrow \frac{\mu}{\infty}-\frac{1}{(-x)}=\frac{\mu-1}{+R}=+\frac{1}{x}=\frac{\mu-1}{R}$
$\therefore x=+\left(\frac{R}{\mu-1}\right)=\frac{R}{(\mu-1)}$