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  • For paraxial rays, show that the focal length of a spherical mirror is one-half of its radius of curvature.       <div style="float:l

For paraxial rays, show that the focal length of a spherical mirror is one-half of its radius of curvature.

 

 

 
 
 
 
 

Answers (1)

 

from the ray diagram, we have 

\tan \theta =\frac{MD}{CD} and \tan 2\theta =\frac{MD}{FD}

For the small \theta

\tan \theta \cong \theta ,\; \; \; \tan 2\theta =\frac{MD}{FD}

therefore, \frac{MD}{FD}=2\frac{MD}{CD}

FD=\frac{CD}{2}\cong \frac{CP}{2}

Hence, F=\frac{R}{2}  So, it can be seen that the focal length of a spherical mirror is one-half of its radius of curvature,

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