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Question

The focal length f is related to the radius of curvature r of the spherical convex mirror by:


A

f=r

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B

f=-12r

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C

f=+12r

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D

f=-r

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Solution

The correct option is C

f=+12r


Step 1: Given data:

Focal length=F

Center of curvature=C

Step 2: Formula used:

When the subject is in focus, the focal lengthf of the lens is the distance between the optical center and the focus, commonly expressed in millimeters.

The radius of curvaturer is the radius of the convex or concave mirror's sphere. It's also the same as the distance between the optical center and the curvature's center.

Step 3: Calculation:

The radius of curvature for spherical mirrors with narrow apertures is found to be double the focal length. A spherical mirror's principal focus lies at the center, between the center of curvature and the optical center and the focal length of a convex lens is positive.

r=2ff=r2

Hence, option C is the correct answer.


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