88.6k views
5 votes
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?

1 Answer

5 votes

Answer:

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.

User Samadhan Medge
by
6.7k points