A concave mirror has a radius of curvature of 24 cm. How far is
an object from the mirror if an image is formed that is:
(a) virtual and 3.0 times the size of the object,
(b) real and 3.0 times the size of the object and
(c) real and `1//3` the size of the object?.

Answer

A, B, C, D

Explanation

Given ,`R=-24 cm` (concave mirror)
Hence , `f=(R/2)=-12cm`
(a) Image is virtual and 3 times larger, u is nagative and v is positive.
Simultaneously ,`|v|=3|u}`.So, let,
`u=-x`
then `v=+3x`
Substituting in the mirror formula,
` 1/v+1/u=1/f`
We have,
` 1/(3x)-1/x=1/(-12)`
`:. x=8cm.`
Therefor , object distance is 8 cm.
(b) Image is real and three times larger. Hence, u and v both are negative and `|v|=3|u|.`
so let,
` u=-x`
then `v=-3x`
Substituting in mirror formula ,we have
`(1/(-3x))+1/x=-(1)/(12)`
or `x=16cm`
`:.` Object distance should be 10cm.
(c ) Image is real and (1/3)rd the size of object. Hence ,both u and v are negative and `|v|=(|u|)/(3).`
So let , u=-x
then `v=-(x/3)`
Substituting in the formula, we have
` -(3/x)-(1/x)=-(1/12)`
` :. x=48 cm`
`:.` Object distance should be `48cm`.