Two prisms of identical geometrical shape are combined with their refracting angles oppositely directed. The materials of the prisms have refractive indices 1.52 and 1.62 for violet light. A violet ray is deviated by ${1.0}^{\circ}$ when passes symmetrically through this combination. What is the angle of the prisms ?

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Solution

Two prisms of identical geometrical shape are combined

Let A = Angle of the prisms

$μ_{y}$ = 1.52 and $μ_{y}$ = 1.62

$μ_{y} = {1.0}^{\circ}$

$δ_{y} = (μ_{y} - 1) A - (μ_{y} - 1) A$ [since A = $α$ ]

$δ_{y} = (μ_{y} - μ_{y}) A$

$A = \frac{δ_{y}}{μ_{y} - μ_{y}} = \frac{1}{(1.62) - (1.52)}$

$= \frac{1}{(0.1)} = 10^{\circ}$

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Column IColumn II(P)The prisms are made of same material and their refracting(1) No deviation,No dispersionangles are equal,ie.,A=A′.The combination will cause(Q)The prisms are made of same material and their refractingangles are not equal,i.e.,A≠A′.The combination will(2) No deviation,Dispersion happenscause.(R)The prisms are made of different material and theirrefracting angles are equali.e.A=A′.Also the quantityμv−μg has different values for the two prisms. Here(3)No dispersion,deviation happensμv and μg are the refractive indices for violet and redcolours.The combination will cause.(S)The prisms are made of different materials and theirrefracting angles are unequal,i.e,A≠A′.AlsoAA′=−(μ′−1)μ−1, where μ is the refractive index for the(4) Both deviation and dispersion happensmean wavelength (yellow) for prism X while μ is thecorresponding value for prism Y.The combination willcause.

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