Question

A man has a shaving mirror of focal length 0.2m.how far should the mirror be held from his face in order to give an image of two fold magnification?

Answer 1

Hello Dear.

Here is the answer---

Given⇒

Focal length of the Mirror = 0.2 m.(negative)
[∵ The Mirror is Concave]

As per as the Question,
Magnification = 2

∵  m = -v/u
∴ 2 × u = -v
∴ v = -2u

Now,
 Using the Mirror's Formula,

   $\frac{1}{f} = \frac{1}{v} + \frac{1}{u}$
⇒ $\frac{1}{- 0.2} = \frac{1}{-2u} + \frac{1}{u}$
⇒ -u = 1/10
⇒ u = - 0.1 m.


Hence, the Man is standing at the Distance of 0.1 m or 10 cm from the Shaving Mirror.


Hope it helps.

Answer 2

f= 0.2m (negative) {follow sign convection}

m=2

Short cut formula is

m=f/f-u

2=0.2/0.2-u

2(0.2-u)=0.2

2u =0.2

u=0.1m !!!

Hope this helps u!♥️