Question 78: Ray Optics

Question

A biconvex lens is formed by using two thin planoconvex lenses, as shown in the figure. The refractive index and radius of curved surfaces are also mentioned in figure. When an object is placed on the left side of lens at a distance of 30 cm from the biconvex lens, the magnification of the image will be :

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).

Answer

−2

Answer

−2.5

Answer

+2.5

Answer

+2

Ray Optics

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