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Ray Optics

JEE Main level, numerical answer, medium

260 of 295

Question 260 of 295

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 are $0.02$ 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)

Show answer and solution

Answer: 12

{\omega }_{1}=0.02;{\mu }_{1}=1.5;{\omega }_{2}=0.03;{\mu }_{2}=1.6

Achromatic combination

∴{\theta }_{net}=0

{\theta }_{1}-{\theta }_{2}=0

{\theta }_{1}={\theta }_{2}

{\omega }_{1}{\delta }_{1}={\omega }_{2}{\delta }_{2}

and

{\delta }_{net}={\delta }_{1}-{\delta }_{2}=2^{\circ}

{\delta }_{1}-\dfrac{{\omega }_{1}{\delta }_{1}}{{\omega }_{2}}=2^{\circ}

{\delta }_{1}\left(1-\dfrac{{\omega }_{1}}{{\omega }_{2}}\right)=2^{\circ}

{\delta }_{1}\left(1-\dfrac{2}{3}\right)=2^{\circ}

{\delta }_{1}=6^{\circ}

{\delta }_{1}=\left({\mu }_{1}-1\right){A}_{1}

6^{\circ}=\left(1.5-1\right){A}_{1}

{A}_{1}=12^{\circ}

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JEE Main 2025 Apr 2 Shift 1 question paper

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