Question

A point object is kept between a plane mirror and a concave mirror facing each other. The distance between the mirrors is $22.5cm$. Plane mirror is placed perpendicular to principal axis of concave mirror. The radius of curvature of the concave mirror is $20cm$. What should be the distance of the object from the concave mirror so that after two successive reflections the final image is formed on the object itself? (Consider first reflection from concave mirror)

• A. $5cm$
• B. $15cm$
• C. $10cm$
• D. $7.5cm$

Answer 1

The correct option is B $15cm$

Concave mirror(flat reflection),

$\frac{1}{v}+\frac{1}{u}=\frac{1}{f}\frac{1}{-(45-x)}+\frac{1}{-x}=\frac{1}{-10}\frac{1}{45-x}+\frac{1}{x}=\frac{1}{10}\frac{x+45-x}{(45-x)x}=\frac{1}{10}450=45x-x^2{orx}^2-45x+450=0{orx}^2-15x-30x+450=0or(x-15)-30(x-15)=0or(x-15)(x-30)=0x=15;x=30$

$x=30$ Not possible as distance between mirrors only $22.5cm$