Question

A candle flame 3cm high is placed at a distance of 3m from wall.how far from the wall must a concave mirror be placed so that it may form 9cm high image of the flame on the same wall?Also find the focal length of the mirror.​

Answer 1

concave mirror is placed say x distance from the candle.

So screen, I mean wall, will be at 3 + x m distance

Given magnification 3 = v/u = (3 + x) / x

Or 3 x = 3 + x

x = 1.5 m

Concave mirror is to be placed at a distance 4.5 m from the wall

Focal length = uv /(u+v) = 1.5 * 4.5 / 6 = 4.5/4 m

Ans = 1.125 m

Answer 2

Explanation:

Let

A'p=3+x metre

So,

• u=-xm
• v=-(x+3)m

As we know that

$\boxed{\sf m=\dfrac{-v}{u}}$

$\\ \qquad\quad\sf{:}\longrightarrow \dfrac{-9}{3}$

$\\ \qquad\quad\sf{:}\longrightarrow \dfrac{-x+3}{x}$

$\\ \qquad\quad\bf{:}\longrightarrow x=1.5m$

Now,

• u=-1.5m
• v=-4.5m

We know that

$\boxed{\sf \dfrac{1}{f}=\dfrac{1}{u}+\dfrac{1}{v}}$

$\\ \qquad\quad\sf{:}\longrightarrow \dfrac{-1}{1.5}-\dfrac{1}{4.5}$

$\\ \qquad\quad\sf{:}\longrightarrow \dfrac{-8}{9}$

$\\ \qquad\quad\bf{:}\longrightarrow f=-1.125m$