Physics - Geometrical Optics Question with Solution | TestHub

Let $f$ be the focal length

Given $m=\frac{1}{3}$ and $v=8$ m

$m=\frac{v}{u}$, so $u=3v=24$ m

Using the lens formula, $\frac{1}{f}=\frac{1}{v}+\frac{1}{u}=\frac{1}{8}+\frac{1}{24}=\frac{4}{24}=\frac{1}{6}$

Thus, $f=6$ m

Now, $\mu =\frac{3}{2}$, and using lens maker's formula, $\frac{1}{f}=(\mu -1)(\frac{1}{R_1}-\frac{1}{R_2})$.

Since it is a plano-convex lens, one surface is flat (say $R_2=\infty$)

so $\frac{1}{6}=(\frac{3}{2}-1)(\frac{1}{R})$

$\frac{1}{6}=\frac{1}{2R}$. Therefore, $R=3$ m.