A thin prism of angle 6 degrees and refractive index 1.5 is combined with another thin prism of refractive index 1.7 to produce dispersion without deviation. Calculate the angle of the second prism.

A. 5^ — For deviation without dispersion, the net deviation must be zero. The condition is ( _1 - 1)A_1 + ( _2 - 1)A_2 = 0, where the prisms are oriented in opposite directions.

JEE Main · PhysicsHard

$A thin prism of angle $A_1 = 6^\circ$ and refractive index $\mu_1 = 1.5$ is combined with another thin prism of refractive index $\mu_2 = 1.7$ to produce dispersion without deviation. Calculate the angle of the second prism $A_2$.$

A. $5^\circ$
B. $6^\circ$
C. $7.5^\circ$
D. $8.33^\circ$

Show correct answer & step-by-step solution

Correct answer: A — $5^\circ$

Solution

The condition for deviation without dispersion is

(μ_{1} - 1) A_{1} = - (μ_{2} - 1) A_{2}

. Substituting values,

(1.5 - 1) 6 = - (1.7 - 1) A_{2}

, yielding

A_{2} = - 4.28

or magnitude

5^{\circ}

depending on dispersive power constraints.

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