Question

A rod of length $2 \,cm$ makes an angle $\frac{2 \pi}{3}$ 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 $\frac{40}{3} cm$ from the object as shown in the figure The height of the image is $\frac{30 \sqrt{3}}{13} cm$ and the angle made by it with respect to the principal axis is $\alpha rad$ The value of $\alpha$ is $\frac{\pi}{n} rad$, where $n$ is ___

Answer 1

$\frac{ h _i}{h_0} ​= \frac{ v}{u} ⇒ \frac{\frac{-30\sqrt{3}}{13}}{\sqrt{3}}= \frac{v}{\frac{-43}{3}}⇒v _ 1 ​ = \frac{430}{13} cm$

$\frac{1}{v}-\frac{1}{u}=\frac{1}{f}$
$⇒ \frac{1}{v}=\frac{1}{10}-\frac{3}{40}$
⇒$$v=40 cm

$x=40-\frac{430}{13}=\frac{90}{13} cm$

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

⇒$$\alpha=30\degree=\frac{\pi}{6}
N=6