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If the refracting angle of a prism is A,...

If the refracting angle of a prism is A, the refractive index of its material is `mu` and the angle of deviation of a ray of light incident normally on the first refraction face is `delta`, then prove that `mu = sin(A + delta)/(sinA).`

Text Solution

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Angle of deviation for refraction in the prism, `delta = i_(1) + i_(2) - A and A = r_(2) + r_(2)`
`"For normal incidence" " " i_(1) = 0 and r_(2) = 0`
`therefore " " delta = i_(@) - A or, i_(2) = A + delta`
`and A = r_(2)`
`therefore "Refractive index of the prism",`
`mu = (sini_(2))/(sinr_(2)) = (sin(A + delta))/(sinA)`
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