A rod of length 2 cm makes an angle 2 π/3 rad with the principal axis of a thin convex lens. The lens has a focal length of 10 cm and is placed at a distance of 40/3 cm from the object as shown in the figure, The is frac 30 √(3) 13 and the angle made by it with respect to the principal axis is α rad. The value of α is π/n rad , where n is

Physics · Geometrical Optics

JEE Advanced 2022 — Paper 1 — Question 22

A rod of length 2 cm makes an angle $\frac{2 \pi}{3} \mathrm{rad}$ with the principal axis of a thin convex lens.

The lens has a focal length of 10 cm and is placed at a distance of $\frac{40}{3} \mathrm{~cm}$ from the object as shown in the figure,

The is $\frac{30 \sqrt{3}}{13}$ and the angle made by it with respect to the principal axis is $\alpha$ rad.

The value of $\alpha$ is $\frac{\pi}{n} \mathrm{rad}$ , where n is $\qquad$

Numerical answer — enter this value.

$u_{1}=-\frac{40}{3}$

$\mathrm{f}=10$

$\frac{1}{\mathrm{~V}_{1}}+\frac{1 \times 3}{40}=\frac{1}{10}$

$\mathrm{V}_{1}=40$

$u_{2}=-\frac{43}{3}$

$\frac{1}{\mathrm{~V}_{2}}=\frac{1}{10}-\frac{3}{43}=\frac{43-30}{430}$

$\mathrm{V}_{2}=\frac{430}{13}$

$x_{2}=V_{1}-V_{2}=40-\frac{430}{13}=\frac{90}{13}$

$\tan \alpha=\frac{30 \sqrt{3}}{13 \times x}=\frac{30 \sqrt{3} \times 13}{13 \times 90}=\frac{1}{\sqrt{3}}$

$\alpha=\frac{\pi}{6}=\frac{\pi}{n}$ $\mathrm{n}=6$

Answer key and solution verified before publishing.

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