Question

Match the following columns.
Four combination of two thin lenses are given in List $I$. The radius of curvature of all curved surface is $r$ and the refractive index of all the lenses is $1.5$. Match lens combination in List $I$ with their focal legth in List $II$ and selected the correct answer using the code given below the lists.

Answer 1

$\Rightarrow \frac{1}{f}=\left(\frac{\mu -1}{r}\right)+\left(\frac{1-\mu }{-r}\right)+\left(\frac{\mu -1}{r}\right)+\left(\frac{1-\mu }{-r}\right)$

$\Rightarrow \mu =1.5$

$=\left(\frac{0.5}{r}\right)+\left(\frac{0.5}{r}\right)+\left(\frac{0.5}{r}\right)+\left(\frac{0.5}{r}\right)$

$=\frac{2}{r}$

$\Rightarrow f=\frac{r}{2}.$

$\Rightarrow \frac{1}{f}=\left(\frac{\mu -1}{\infty }\right)+\left(\frac{1-\mu }{-r}\right)+\left(\frac{\mu -1}{r}\right)+\left(\frac{1-\mu }{\infty }\right)$

$\Rightarrow \frac{1}{f}=\left(\frac{0.5}{r}\right)+\left(\frac{0.5}{r}\right)=\frac{1}{r}$

$\Rightarrow f=r.$

$\Rightarrow \frac{1}{f}=\left(\frac{\mu -1}{\infty }\right)+\left(\frac{1-\mu }{r}\right)+\left(\frac{\mu -1}{-r}\right)+\left(\frac{1-\mu }{\infty }\right)$

$\Rightarrow \frac{1}{f}=\left(\frac{-0.5}{r}\right)+\left(\frac{0.5}{-r}\right)=\frac{-1}{r}$

$\Rightarrow f=-r.$

$\Rightarrow \frac{1}{f}=\left(\frac{\mu -1}{r}\right)+\left(\frac{1-\mu }{-r}\right)+\left(\frac{\mu -1}{\infty }\right)+\left(\frac{1-\mu }{r}\right)$

$\Rightarrow \frac{1}{f}=\left(\frac{0.5}{r}\right)+\left(\frac{0.5}{-r}\right)+\left(\frac{-0.5}{r}\right)=\frac{0.5}{r}$

$\Rightarrow f=2r.$

Hence, solved.