Please derive the formula for angle …

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Please derive the formula for angle of deviation in a glass prism.

Posted by Adarsh Anand 6 years, 3 months ago

CBSE > Class 10 > Science

1 answers

Sia ? 6 years, 3 months ago

The relationship between refractive index {tex}\mu{/tex}, prism angle A and angle of minimum deviation {tex}\delta_m{/tex} is given by
{tex}\mu = \frac { \sin \left[ \left( A + \delta _ { m } \right) / 2 \right] } { \sin ( A / 2 ) }{/tex}
Given, {tex}\delta _ { m } = A{/tex}
Substituting the value of {tex}\delta_m{/tex}, we have
{tex}\therefore \mu = \frac { \sin A } { \sin ( A/ 2 ) }{/tex}
On solving, we have
{tex}\mu = \frac { 2 \sin \frac { A } { 2 } \cos \frac { A } { 2 } } { \sin \frac { A } { 2 } } = 2 \cos \frac { A } { 2 }{/tex}
For the given value of refractive index,{tex}\mu = \sqrt { 3 }{/tex}, we have
{tex}\cos \frac { A } { 2 } = \frac { \sqrt { 3 } } { 2 } \text { or } \frac { A } { 2 } = 30{/tex}
A = 60°
This is the required value of prism angle.

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Posted by Pandey Ji 5 months, 3 weeks ago

CBSE > Class 10 > Science