Question

An object is placed at a distance of $25cm$ from the pole of a convex mirror and a plane mirror is set at a distance $5cm$ from the convex mirror so that the virtual images formed by the two mirrors do not have any parallax. The focal length of the convex mirror is :

• A. $37.5cm$
• B. $-7.5cm$
• C. $-37.5cm$
• D. $+7.5cm$

Answer 1

Answer: (A)

$37.5cm$

The image formed by the plane mirror as well as by the convex mirror is at $I$.

Distance between object and plane mirror is $(25-5)cm=20cm$

$\therefore$ Distance between plane mirror and the image $MI=20cm⟹PI=v=+15cm$

Let the focal length of the convex mirror be $fcm.$

Using mirror formula, $\frac{1}{v}+\frac{1}{u}=\frac{1}{f}$

$\therefore \frac{1}{15}+\frac{1}{-25}=\frac{1}{f}$

$⟹f=+37.5cm$