Question

Ram was playing with a convex mirror and a plane mirror. When an object AB is placed in front of the mirrors he could see two virtual images. When the object is placed at a position as shown in the figure, he found that both the images coincide with each other. If the focal length of the convex mirror is $30$ cm, find the value of 'x'.

• A. $80$ cm
• B. $40$ cm
• C. $60$ cm
• D. $30$ cm

Answer 1

The correct option is B $40$ cm

For plane mirror-

Distance of image from mirror$=v_1=x$

For convex mirror, distance of image from convex mirror is $v$.

And, for images to coincide-

$v_1=v+20⟹v=x-20$

$\frac{1}{v}+\frac{1}{u}=\frac{1}{f}$

$⟹\frac{1}{v}+\frac{1}{-(20+x)}=\frac{1}{30}$

$⟹\frac{1}{x-20}-\frac{1}{x+20}=\frac{1}{30}$

$⟹\frac{x+20-x+20}{(x-20)(x+20)}=\frac{1}{30}$

$⟹(x-20)(x+20)=40\times 30=1200$

$⟹x^2=1600$

Solving the equation, we get $x=40cm$