Question

A concave mirror having a radius of curvature 40 cm is placed in front of an illuminated point source at a distance 30 cm from it. Find the location of the image.

• A. 40 cm , behind the mirror
• B. 60 cm, on the side of the object
• C. 40 cm, on the side of the object
• D. 60 cm, behind the mirror.

Answer 1

The correct option is B 60 cm, on the side of the object

Let's look at the schematic first.

We have,
$f=-20cm.(recall,f=\frac{R}{2})u=-30cm.Usingmirrorformula\frac{1}{u}+\frac{1}{v}=\frac{1}{f}Or,\frac{1}{v}=\frac{1}{f}-\frac{1}{u}Substitutingthevalues;\frac{1}{v}=\frac{-1}{20}-\frac{-1}{30}=\frac{-1}{20}+\frac{-1}{30}Weget,\frac{1}{v}=\frac{-1}{60}c{m}^{-1}$
Hence,
v=−60 cm  or 60 cm ,on the side of the object
(A negative value of v means that the  image is on the opposite side of the incident ray).