Question

an object is placed infront of a concave mirror of focal length 20 cm. the image formed is 3 times the size of the object. calculate 2 possible distances from the mirror ​

Answer 1

$\mathbb{\underline{\underline{ANSWER}}}$

Given:-

f = -20cm

m = -3 or 3 (-ve since it is a concave mirror) {m is positive if object is placed between P and F}

                                                                                                 

As, we know {for -3}

m = $\frac{-v}{u}$

-3 =  $\frac{-v}{u}$

-3u = -v

3u = v

                                                                                                   

Using mirror formula we get,

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

Substituting v = 3u in the equation we get,

$\frac{1}{3u}$ + $\frac{1}{u}$ = $\frac{1}{-20}$

$\frac{3u + u}{3u²}$ = $\frac{-1}{20}$

4u(20) = -3u²

80 u + 3u² = 0

3u²+80u = 0

u(3u + 80) = 0

u = 0 or u = -80/3

∵ u ≠ 0 ⇒ u = -80/3

                                                                                                 

Let m = 3

Then,

3u = -v

v = -3u

                                                                           

Substituting v = -3u in the mirror formula we get,

$\frac{-1}{3u}$ + $\frac{1}{u}$ = $\frac{-1}{20}$

$\frac{-u+3u}{3u²}$ = $\frac{-1}{20}$

$\frac{2u}{3u²}$ = $\frac{-1}{20}$

40u = -3u²

3u²+40u = 0

u(3u+40) = 0

u = 0 or u = -40/3

∵ u ≠ 0 ⇒ u = -80/3

                                                                                   

The two possible places for the object can be placed is

$\boxed{u=-80/3\:or\:u=-40/3}$

Answer 2

REFER TO ATTATCHMENT FOR YOUR ANSWER. . .