Question

FIND THE DISTANCE OF THE OBJECT FROM A CONCAVE MIRROR OF FOCAL LENGTH 10 CM SO THAT IMAGE SIZE IS 4 TIMES THE SIZE OF THE OBJECT

Answer 1

Answer:

The answer is 12.5 cm....

Step-by-step explanation:

Let the distance of the object from the concave mirror be u and let the distance of the image be v.

Focal length of the mirror = f = -10 cm

Since the image is 4 times the size of the object, the image formed is real and inverted in nature and hence, the magnification is negative.

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

$\Rightarrow -4\: = \: \frac{-v}{u}\\ \Rightarrow 4\: =\: \frac{v}{u}\\ \Rightarrow v\: = \: 4u$

According to mirror formula,

$\frac{1}{f}\: =\: \frac{1}{V}+\frac{1}{U}\\ \Rightarrow \frac{1}{f}\: =\: \frac{1}{-v}+\frac{1}{-u}\: (\because\: v,\: and\: u\: are\: negative)\\ \Rightarrow \frac{1}{f}\: = \: -\frac{1}{v}-\frac{1}{u}\\ \Rightarrow \frac{1}{f}\: =\: -(\frac{1}{4u}+\frac{1}{u})\: (\because\: v=4u)\\ \Rightarrow \frac{1}{-10}\: =\: -(\frac{1+4}{4u})\\ \Rightarrow \frac{1}{-10}\: =\: \frac{-5}{4u}\\ \Rightarrow \frac{4u}{-10}\: =\: -5\\ \Rightarrow u\: =\: \frac{(-5)×(-10)}{4}\\ \Rightarrow u\: =\: 12.5 \: cm$

Answer 2

Answer:

option a) is the correct answer 1.25cm

Step-by-step explanation:

size of the image by size of the object

1.25 is the multi option

correct answer is 1.25cm