Question

A thin prism Pof angle 4° and refractive index 1.54 is combined with another thin prism Pzof refractive index 1.72 to produce dispersion without deviation. The angle of prism Pis​

Answer 1

The angle of prism P is 4°, and the angle of prism Q is 0°, and they are combined to produce dispersion without deviation.

Given:

Pof = 4°

refractive index = 1.54

Pzof refractive index = 1.72

To Find:

Angle of prism P and Q

Solution:

When two thin prisms are combined, the net deviation caused by them is given by:

δ = (A - B)μ

where A and B are the angles of the two prisms, and μ is the refractive index of the material of the prism.

Since we wish to create dispersion in this situation without any deviation, the net deviation brought on by the two prisms should be zero. Since we are aware of the two prisms' refractive indices, we may write:

(A - B)μP + (C - D)μQ = 0

where μP = 1.54 is the refractive index of prism P, and μQ = 1.72 is the refractive index of prism Q. We also know that the angle of prism Q is zero, because it is not causing any deviation.

Substituting the values, we get:

(A - B)(1.54) + (C - 0)(1.72) = 0

Simplifying, we get:

1.54A - 1.54B + 1.72C = 0

We also know that the angle of prism P is 4°, so A = 4° and B = -4°. Substituting these values, we get:

(1.54)(4°) - (1.54)(-4°) + (1.72)C = 0

Simplifying, we get:

C = 4.16°

Therefore, the angle of prism P is 4°, and the angle of prism Q is 0°, and they are combined to produce dispersion without deviation.

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