Question

A rod of length 10 cm lies along the principal axis of a concave mirror of focal length 10 cm in such a way that the end closer to the pole is 20 cm away from it.
Find the length of the image.

• A. 10 cm
• B. 8 cm
• C. 5 cm
• D. None of these

Answer 1

The correct option is C 5 cm

So, the idea to form the image of the extended object lying on the principal axis is to get the image of the two extreme points of the object and join these two points.
Let's draw the schematic first.

Let's take the two extreme points A & B.
The end B of the rod is at the center of curvature and hence its image will be formed at the center of curvature itself. Let's locate the image of point A.
For point A we have,
u = − 30cm and f = −10cm.
We have mirror formula,
$\frac{1}{u}+\frac{1}{v}=\frac{1}{f}Or,\frac{1}{v}=\frac{1}{f}-\frac{1}{u}=-\frac{1}{10}-\frac{1}{30}Weget,v=-15cm.$
Thus, the image is formed at a distance 15cm from the pole.

From the diagram below we see that the length of the image is 5 cm.