JEE Main · 2021 · 16 Mar 2021 · Shift 2 · Geometrical Optics

A deviation of

2^{0}

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 will be ____

^{0}

. (in degree) Round off to the Nearest Integer)

Answer: 12

Solution

Let

δ_{1}

and

δ_{2}

be the deviations the crown and the flint prism produce in yellow light. An achromatic pair is one whose dispersions cancel, which requires

ω_{1} δ_{1} = ω_{2} δ_{2} \Rightarrow 0.02 δ_{1} = 0.03 δ_{2} \Rightarrow δ_{2} = \frac{2}{3} δ_{1}

The two prisms are set in opposite senses, so the deviations subtract and the surviving deviation of the yellow ray is

δ_{1} - δ_{2} = δ_{1} - \frac{2}{3} δ_{1} = \frac{δ _{1}}{3} = 2^{\circ}

which gives

δ_{1} = 6^{\circ}

. For a thin prism

δ_{1} = (μ_{1} - 1) A_{1}

, so

A_{1} = \frac{6 ^{\circ}}{1.5 - 1} = 1 2^{\circ}

The refracting angle of the crown glass prism is

1 2^{\circ}

JEE Main · 2021 · 16 Mar 2021 · Shift 2 · Integer answer

Practise more: all JEE Main PYQs on Geometrical Optics →

JEE Main · 2021 · 16 Mar 2021 · Shift 2 · Geometrical Optics

Solution

More JEE Main questions on Geometrical Optics