Question

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

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

Answer 1

The correct option is A $25cm$

As shown in figure, the plane mirror will form erect and virtual image of same size at a distance of $30cm$ behind it. So, the distance of image formed by plane mirror from convex mirror will be
$PI=MI-MP$
But as, $MI=MO$
$PI=MO-MP=30-20=10cm$
Now, as this image coincides with the image formed by convex mirror, therefore for convex mirror,
$u=-50cm;v=+10cm$
So, $\frac{1}{+10}+\frac{1}{-50}=\frac{1}{f}$, i.e., $f=\frac{50}{4}=12.5cm$
So, $R=2f=2\times 12.5=25cm$.