Question

The image of an object placed on the principal axis of a concave mirror of focal length 12 cm is formed at a point which is 10cm more distance form the mirror than the object. The magnification of the image is
A. `8//3`
B. 2.5
C. 2
D. `-1.5`

Answer 1

Correct Answer - d.
Let `u=-x`
`(1)/(-x)+(1)/(-x-10)=-(1)/(12)`
or `(1)/(x)+(1)/(x+10)=(1)/(12)`
or `(x+10+x)/(x(x+10))=(1)/(12)`
or`(2x+10)/(x^(2)+10x)=(1)/(12)`
or `x^(2)+10x=24x+120`
or `x^(2)-14x-120=0`
`x^(2)-20x+6x-120=0`
or `x(x+20)+6(x-20)=0`
Here `u=-20cm`
`u=-(20+10)CM =-30cm`
Then magnification
`m=-(u)/(v)`
`=-((-30)/(-20))`
=`1.5`