A plano-convex lens fits exactly into a plano | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) The combination of two lenses $1$ and $2$ is as shown in the figure.For a combination of thin lenses in contact,the equivalent focal length $f$ is

Vedclass · Accepted Answer

$\frac{R}{(\mu_1 - \mu_2)}$

Vedclass · Answer

(C) The combination of two lenses $1$ and $2$ is as shown in the figure.For a combination of thin lenses in contact,the equivalent focal length $f$ is given by $\frac{1}{f} = \frac{1}{f_1} + \frac{1}{f_2}$.According to the lens maker's formula,$\frac{1}{f} = (\mu - 1) \left( \frac{1}{R_1} - \frac{1}{R_2} \right)$.For the plano-convex lens (lens $1$): $R_1 = \infty$,$R_2 = -R$. Thus,$\frac{1}{f_1} = (\mu_1 - 1) \left( \frac{1}{\infty} - \frac{1}{-R} \right) = \frac{\mu_1 - 1}{R}$.For the plano-concave lens (lens $2$): $R_1 = -R$,$R_2 = \infty$. Thus,$\frac{1}{f_2} = (\mu_2 - 1) \left( \frac{1}{-R} - \frac{1}{\infty} \right) = -\frac{\mu_2 - 1}{R}$.Substituting these into the combination formula:$\frac{1}{f} = \frac{\mu_1 - 1}{R} - \frac{\mu_2 - 1}{R} = \frac{\mu_1 - 1 - \mu_2 + 1}{R} = \frac{\mu_1 - \mu_2}{R}$.Therefore,$f = \frac{R}{\mu_1 - \mu_2}$.

Similar Questions

The ratio of the dispersive powers of two lenses is $4:3$. If the achromatic combination of these two lenses in contact is a convex lens of focal length $60 \, cm$,find the focal lengths of the component lenses.

$A$ glass convex lens of focal length $0.1 \ m$ is cut into two equal parts along its axis. The ratio of the focal length of the new lenses is:

The position of the final image formed by the given lens combination from the third lens will be at a distance of $(f_1 = +10 \ cm, f_2 = -10 \ cm, f_3 = +30 \ cm)$.

$A$ magnifying glass is made of a combination of lenses with power $+20\,D$ and $-4\,D$. If the least distance of distinct vision is $25\,cm$,calculate the size of an image of an object $2\,cm$ high seen through the magnifying glass. (in $,cm$)

An achromatic convergent doublet of two lenses in contact has a power of $+2 \ D$. The convex lens has a power of $+5 \ D$. What is the ratio of the dispersive powers of the convergent and divergent lenses?

Vedclass Test Series

Exam Paper Generator

Online Exam Module