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Question

# A crown glass prism of refracting angle 80 is combined with a flint glass prism to obtain deviation without dispersion. If the refractive indices for red and violet rays for the crown glass are 1.514 and 1.524 and for the flint glass are 1.645 and 1.665 respectively, the net deviation is

A
1.530
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B
1.230
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C
1.440
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D
1.140
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Solution

## The correct option is B 1.230Angle of crown glass prism (A)=8∘ For crownμγ=1.514μV=1.524,μ=1.514+1.5242=1.5195For flint glassμ′γ=1.645μ′v=1.665,μ′=1.645+1.6652=1.650Condition for no dispersion is.-) deviation in crown = devition in flint glassdv−dγ=d′v−dγ⇒(μV−μγ)A=(μ′v−μ′γγ)A′A′= angle in flint glass (1.52.5−1.514)8=(1.665−1.645)A′0.011×8=0.020×n′∴A′=0,011×80,020∴A′=4.40 Mean deviation =d−d′=(μ−1)A−(μ′−1)R′=[μ,μ′ are avg values }=(1.5195−1)8−(1.650−1)4.4=0.5195×8−0.650×4.4=4.156−2.86⇒1.296≈1.23( nearest ) Hence (B) is correct option.

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