Question

A convex lens forms a real image three times larger than the object on a screen. Object and screen are moved until the image becomes twice the size of the object. If the shift of the object is $6cm.$ The shift of screen is

• A. $36cm$
• B. $72cm$
• C. $18cm$
• D. $9cm$

Answer 1

The correct option is A $36cm$

$\frac{1}{3x}+\frac{1}{x}=\frac{1}{f}$

$\frac{4}{3x}=\frac{1}{f}$ ……..$\left(1\right)$

$\Rightarrow \frac{1}{2(6+x)}+\frac{1}{6+x}=\frac{1}{f}$

$\Rightarrow \frac{3}{2(6+x)}=\frac{1}{f}$ …….$\left(2\right)$

From equation $\left(1\right)$ & $\left(2\right)$

$\frac{4}{3x}=\frac{3}{2(6+x)}$

$\Rightarrow 9x=48+8x$

$x=48$

Shift of screen$=3x-2(6+x)$

$=3\times 48-2(6+48)$

$=36$cm

Answer is A.