Question

What is the focal length of a mirror if an object placed 21 cm from it produces an image that is magnified -0.85X? What is the power of the mirror?

Answer 1

focal length is 9.65 cm and the power is 10.36 diopter.

Step-by-step explanation:

Now consider the case of concave mirror according to sign convention

`u=21 cm`

And the magnification produced buy it is,

`m=-0.85`

Therefore,

`m=-(v)/(u) \\-0.85=-(v)/(21) \\v=(21* 0.85)`

Now focal length is,

`(1)/(f) =(1)/(v)+(1)/(u)  \\(1)/(f) =(1)/(21(0.85))+(1)/(21)\\(1)/(f) =(1)/(21)((1.85)/(0.85))\\ f=9.65 cm`

Therefore the focal length is 9.65 cm.

Now, the power is,

`P=(1)/(f)`

Therefore,

`P=(1)/(9.65* 10^(-2) )m^(-1) \\P=10.36 diopter`

Therefore the power of the mirror is is 10.36 diopter.