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

Answer:

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

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,

$m=-\frac{v}{u} \\-0.85=-\frac{v}{21} \\v=(21\times 0.85)$

Now focal length is,

$\frac{1}{f} =\frac{1}{v}+\frac{1}{u}  \\\frac{1}{f} =\frac{1}{21(0.85)}+\frac{1}{21}\\\frac{1}{f} =\frac{1}{21}(\frac{1.85}{0.85})\\ f=9.65 cm$

Therefore the focal length is 9.65 cm.

Now, the power is,

$P=\frac{1}{f}$

Therefore,

$P=\frac{1}{9.65\times 10^{-2} }m^{-1} \\P=10.36 diopter$

Therefore the power of the mirror is is 10.36 diopter.