Question

The focal length of a concave mirror is 12cm if the radius of curvature of the mirrors is doubled what it its focal length?

Answer 1

Answer:

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Answer 2

Answer:

The focal length of a concave mirror is 12cm. If the radius of curvature of the mirrors is doubled, its focal length will be $48\ cm$

Explanation:

• The distance from the pole to the center of curvature of the mirror is called the radius of curvature and focal length is the distance between the pole of the mirror and the focus of the object.              

• For spherical mirrors having a small aperture, the radius of curvature is twice the focal length.

• Let R be the radius of curvature and f be the focal length then,

        $R = 2f$     ...(1)

        and  

        $f = \frac{R}{2}$       ...(2)

   

In the question, it is given that,

$f = 12\ cm = 12\times 10^{-2} m$

Substitute  the value of 'f' into equation(1),

We get,

$R = 2\times 12\times10^{-2} = 24\times10^{-2} m = 24\ cm$

If the radius of curvature is doubled,  

$R = 48\times 2 = 96\ cm$

then,  using equation (2),

$f = \frac{96}{2} = 48$ cm