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Deduce Prism equation and find the expression for minimum deviation produced by a prism ?

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Prism equation OR Prism formula OR Refraction through prism—

In a prism there are two refracted surface AB and AC.

Case-I—When a ray of light passes from rare to denser medium it bends towards the normal.

Case-II—When a ray of light passes from denser to rarer medium it bends away from the normal.

In quadiralateral ALKP :—

Eqn (8) is called 1st eqn of prism. Hence angle of prism is the sum total of angle of refraction through both the surface.

Using eqn (8) in (4)

Eqn (9) is called 2nd eqn of prism. It starts that the sum total of angle of incidence & angle of emergence is equal to sum angle of deviation and angle of prism.

Case-III Minimum deviation produced by a prism—

Deviation produced by a prism is the angle b/w extended line of incident ray and emergent ray. For minm deviation produced by prism,

A/C to prism's second relation

A/C to snell's law,

Eqn (9) is the general expression for minimum deviation produced by a prism.

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