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Derive the expression for refractive ind...

Derive the expression for refractive index of the material of the prism in terms of angle of the prism and angle of minimum deviation.

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In cyclic quadrilateral AQMR
Sum of the opposite angles `180^(@)`
`rArr /_ A + /_ M = 180^(@)`
In `Delta QMR ` sum of three angles to `180^(@)`
Condition for minimum deviation the rays passes through the prism are symmetrical .
`i_(1) = i_(2) = i` & `r_(1) = r_(2) = r `
d = D
`A = r_(1) + r_(2) = 2r rArr r = ( A)/( 2)`
`d = i_(1) + i_(2) - A`
`D = i + i - A = 2i - A `
`=2i = A + D i = ( A+D)/( 2) `
Substituting in Snell.s law
`n = ( sin i )/( sin r ) = ( sin ((A+D)/(2)))/( sin ""(A)/( 2))`
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