Ncert Exercises & Solutions

9.2 A 4.5 cm needle is placed 12 cm away from a convex mirror of focal length 15 cm. Give the location of the image and the magnification. Describe what happens as the needle is moved farther from the mirror.

Hint: Use mirror formula
Step 1: Find the location of image.
Object distance, u = -12 cm
The focal length of the convex mirror, f = 15 cm
Let the image distance = v
Now,
$\begin{array}{l} \frac{1}{u} + \frac{1}{v} = \frac{1}{f} \end{array}$
$\frac{1}{v} = \frac{1}{f} - \frac{1}{u} = \frac{1}{15} + \frac{1}{12} = \frac{4 + 5}{60} = \frac{9}{60}$ or,
The image of the needle is formed 6.7 cm away from the mirror. It is on the other side of the mirror.
Step 2: Find the magnification.

$m = \frac{h_{2}}{h_{1}} = - \frac{v}{u}$
The positive sign indicates that the image is erect, virtual, and diminished.

The image moves away from the mirror when the needle is moved farther from the mirror and the size of the image will reduce gradually.

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