Question

A 2.5 cm candle is placed 12cm away from a conversation mirror of focal length30cm give the location of the mirror and magnification

Answer 1

Answer:

location of image = v = 20 cm and

magnification = m = 1.667 (approx)

Explanation:

Given

$h_{i} = 2.5 cm\\ u = 12 cm\\f= 30 cm\\using mirror formula\\\frac{1}{v} + \frac{1}{u} = \frac{1}{f}$

$\frac{1}{v} + \frac{1}{-12} = \frac{1}{-30}$     (applying sign convention , i.e v and f are negative)

$\frac{1}{v} = -\frac{1}{30} + \frac{1}{12}$

$\frac{1}{v} = \frac{-2+5}{60}$       (taking LCM)

$\frac{1}{v} = \frac{3}{60} \\\frac{1}{v} = \frac{1}{20}$        

v=20 . i.e the image will form behind the concave mirror at 20 cm from the pole.

magnification $m=\frac{-v}{u}=\frac{h_{i} }{h_{o} }$

substitute the values of v,u and $h_{i}$

$m=\frac{-(20)}{(-12)} =\frac{20}{12} = 1.667 (apprx)$