question_answer

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 6 cm. The shift of screen is:

A) 36 cm

B) 72 cm

C) 18 cm

D) 9 cm

Correct Answer: A

Solution :

[a] \[\frac{1}{3x}+\frac{1}{x}=\frac{1}{f}\]

or         \[\frac{4}{3x}=\frac{1}{f}\]	...(i)
\[\frac{1}{2(6+x)}+\frac{1}{6+x}=\frac{1}{f}\]
or         \[\frac{3}{2(6+x)}=\frac{1}{f}\]		...(ii)

(i) and (ii) gives \[\frac{4}{3x}=\frac{3}{2(6+x)}\]

\[\therefore \]      \[9x=48+8x\]

\[x=4\text{8 cm}\]

Shift of screen \[=3x-2(6+x)\]\[=3\times 48-2(6+48)\]\[=3\text{6 cm}\]