Question

What is the distance of a needle from a concave mirror of focal length 10cm for which a virtual image of twice its height of formed ?

Answer 1

By formula of magnification..

Answer 2

The distance of the needle from the concave mirror is 5 cm.

The focal length of the concave mirror (f) = 10 cm

Given, the image is virtual and twice its height.

So, the magnification will be (m) = 2

As magnification = height of image / height of object,

                            = - (distance of the image/ distance of the object)

Suppose, the distance of the needle from the concave mirror (object distance) = u

∴ Distance of the image (v) = - 2u

From the mirror formula,

$\frac{1}{v}+ \frac{1}{u}= \frac{1}{f}$

⇒ $\frac{1}{-2u}+ \frac{1}{u}= \frac{1}{-10}$  

⇒ $\frac{1}{2u}$ = $-\frac{1}{10}$

⇒ u = -5

-ve indicates the direction of the object placed.

So, the distance of a needle from a concave mirror of focal length 10cm for which a virtual image of twice its height of formed is 5 cm.