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An Equilateral Glass Prism Has a Refractive Index 1.6 in the Air. Calculate the Angle of Minimum Deviation of the Prism, When Kept in a Medium of Refractive Index 4 √ 2 / 5 . - Physics

Question

Sum

An equilateral glass prism has a refractive index 1.6 in the air. Calculate the angle of minimum deviation of the prism, when kept in a medium of refractive index `4sqrt(2)"/"5.`

Solution

When the prism is kept in another medium we have to take the refractive index of the prism with respect to the provided medium. 

`"medium"^μ = ("μ"_"prism")/("μ"_"medium") = sin[((A + D_m)/2)]/sin(A/2)`

`1.6/((4sqrt(2))/5) = sin[((60^circ + D_m)/2)]/sin(60^circ/2)`

`sqrt(2) = sin[((60^circ + D_m)/2)]/(1/2)`

`sin^-1(1/sqrt(2)) = ((60^circ + D_m)/2)`

`90^circ = 60^circ + D_m`

`D_m = 30^circ`

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