Question

The image of an object formed by a piano-convex lens at a distance of $8m$ behind the lens is real and is one-third the size of the object The wavelength of light inside the lens is $\frac{2}{3}$ times the wavelength in free space the radius of the curved surface of the lens is

• A. $1m$
• B. $2m$
• C. $3m$
• D. $6m$

Answer 1

The correct option is C $3m$

$\begin{array}{c}\text{We Know}\\ \begin{array}{c}\frac{1}{f}=(\mu -1)(\frac{1}{R_1}-\frac{1}{R_2})\\ \frac{1}{f}=(\frac{3}{2}-1)\left(\frac{1}{R}\right)\\ \frac{1}{f}=\frac{1}{2R}\Rightarrow f=2R\end{array}\end{array}$

$\text{given}v=+8m$

$M=\frac{1}{3}=-\frac{v}{u}$

$\begin{array}{cc}\Rightarrow & u=-3v\\ \Rightarrow & u=-24m\end{array}$

$\begin{array}{cc}\frac{1}{f}& =\frac{1}{v}-\frac{1}{u}\\ \frac{1}{2R}& =\frac{1}{8}+\frac{1}{24}\\ \frac{1}{2R}& =\frac{4}{24}\\ R& =3m\end{array}$