Question

An object is placed in front of a convex mirror at a distance of $50 \,cm$. A plane mirror is introduced covering the lower half of the convex mirror. If the distance between the object and the plane mirror is $30 \,cm$, it is found that there is no parallax between the images formed by the two mirrors. What is the radius of curvature of the convex mirror?

• A. 25 cm
• B. 7 cm
• C. 18 cm
• D. 27 cm

Answer 1

Answer: (A)

As shown in figure, the plane mirror will form erect and virtual image of same size at a distance of $30 \,cm$ behind it. So the distance of image formed by plane mirror from convex mirror will be

$P I=M I-M P$
But as, $M I=M O$
$P I=M O-M P=30-20=10 \,cm$
Now as this image coincides with the image formed by convex mirror, therefore for convex mirror,
$u=-50 \,cm ; v=+10 \,cm$
So, $\frac{1}{+10}+\frac{1}{-50}=\frac{1}{f} $ i.e.,
$f=\frac{50}{4}=12.5 \,cm$
So, $R=2 f=2 \times 12.5=2\, cm$