Question 23: Ray Optics

Question

Refer the figure given below. $\mu_1$ and $\mu_2$ are refractive indices of air and lens material. The height of image will be _______ cm.
![](https://app-content.cdn.examgoal.net/fly/@width/image/6y3zli1mnrkvs9w/86adaeda-d665-420c-92bd-dacb288c7479/355b0a40-3421-11f1-b6b2-bf17a61cc83e/file-6y3zli1mnrkvs9x.png?format=png)

Accepted Answer

We use the Lens Maker's Formula for each planoconvex lens :
$\frac{1}{f}=(\mu-1)\left(\frac{1}{R_1}-\frac{1}{R_2}ight)$
For left Plano-convex lens $\left(\mathrm{L}_1ight)$ :
The refractive index of the lens is $\mu_1=1.5$
Radii of curvatures are $\mathrm{R}_1=15 \mathrm{~cm}$ (curved surface), $\mathrm{R}_2=\infty$ (plane surface)
$ \frac{1}{f_1}=(1.5-1)\left(\frac{1}{15}-\frac{1}{\infty}ight)=0.5 	imes \frac{1}{15}=\frac{1}{30} $
$\Rightarrow $ $\mathrm{f}_1=+30 \mathrm{~cm}$
For right Plano-convex lens $\left(\mathrm{L}_2ight)$ :
The refractive index of lens $\mu_2=1.2$
Radii of curvatures are $\mathrm{R}_1=\infty$, (Plane surface) and $\mathrm{R}_2=-12 \mathrm{~cm}$ ( (curved surface)
$ \frac{1}{f_2}=(1.2-1)\left(\frac{1}{\infty}-\frac{1}{-12}ight)=0.2 	imes \frac{1}{12}=\frac{1}{60} $
$\Rightarrow $ $\mathrm{f}_1=+60 \mathrm{~cm}$
Since the lenses are thin and in contact, the total power is the sum of individual powers :
$ \frac{1}{F}=\frac{1}{f_1}+\frac{1}{f_2} $
$\Rightarrow $ $\frac{1}{F}=\frac{1}{30}+\frac{1}{60}=\frac{2+1}{60}=\frac{3}{60}=\frac{1}{20}$
$\Rightarrow $ $\mathrm{F}=+20 \mathrm{~cm}$
Given object distance $\mathrm{u}=-30 \mathrm{~cm}$
Using the Lens Formula: $\frac{1}{\mathrm{v}}-\frac{1}{\mathrm{u}}=\frac{1}{\mathrm{~F}}$
$ \frac{1}{v}-\frac{1}{-30}=\frac{1}{20} $
$\Rightarrow \frac{1}{v}+\frac{1}{30}=\frac{1}{20}$
$\Rightarrow $ $\frac{1}{v}=\frac{1}{20}-\frac{1}{30}=\frac{3-2}{60}=\frac{1}{60}$
$ \mathrm{v}=+60 \mathrm{~cm} $
Magnification for a lens is given by : $\mathrm{m}=\mathrm{v} / \mathrm{u}$
$ m=\frac{60}{-30}=-2 $
The negative sign indicates that the image is real and inverted, and its size is twice the size of the object. Hence, the correct option is (A).
![](https://app-content.cdn.examgoal.net/fly/@width/image/6y3zli1mlbys3ia/87ec5ff0-8832-4a67-a510-fa5de0bbc5ba/9574ba20-03f2-11f1-a285-8fe590341dac/file-6y3zli1mlbys3ib.webp?format=webp)

Answer

1

Answer

0.5

Answer

1.2

Answer

0.25

Ray Optics

Refer the figure given below. \mu_1 and \mu_2 are refractive indices of air and lens material. The height of image will be _______ cm.

Choose the correct answer: