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

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,

## Related Chapters

### Preparation Products

##### Knockout NEET July 2020

An exhaustive E-learning program for the complete preparation of NEET..

₹ 15999/- ₹ 6999/-
##### Rank Booster NEET 2020

This course will help student to be better prepared and study in the right direction for NEET..

₹ 9999/- ₹ 4999/-
##### Knockout JEE Main July 2020

An exhaustive E-learning program for the complete preparation of JEE Main..

₹ 12999/- ₹ 6999/-
##### Test Series NEET July 2020

Take chapter-wise, subject-wise and Complete syllabus mock tests and get in depth analysis of your test..

₹ 4999/- ₹ 2999/-