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QJEEM21Phd077: JEE Main 2021 Physics - Class 12 JEEM21Phd077 Solution: A deviation of 2 is produced in the yellow ray when prism of…

A deviation of 2 ∘^\circ is produced in the yellow ray when prism of crown and flint glass are achromatically combined. Taking dispersive powers of crown and flint glass as 0.02 and 0.03 respectively and refractive index for yellow light for these glasses are 1.5 and 1.6 respectively. The refracting angles for crown glass prism will be ____________ ∘^\circ (in degree). (Round off to the Nearest Integer)

Step-by-Step Verified Solution

δnet=(μ1−1)A1−(μ2−1)A2{\delta _{net}} = ({\mu _1} - 1){A_1} - ({\mu _2} - 1){A_2}

2∘=(μ1−1)A1−(μ2−1)A22^\circ = ({\mu _1} - 1){A_1} - ({\mu _2} - 1){A_2} ....... (1)

and ω1(μ1−1)A1=ω2(μ2−1)A2{\omega _1}({\mu _1} - 1){A_1} = {\omega _2}({\mu _2} - 1){A_2} ..... (2)

Substituting the values in equation (1) and (2), we get

2∘=0.5A1−0.6A22^\circ = 0.5{A_1} - 0.6{A_2} ...... (3)

10A1=18A210{A_1} = 18{A_2} ...... (4)

From equation (3) and (4)

2∘=A12−A132^\circ = {{{A_1}} \over 2} - {{{A_1}} \over 3}

A1=12∘{A_1} = 12^\circ

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