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

(D) For a plano-convex lens with refractive index $n_1$,the focal length $f_1$ is given by the lens maker's formula: $\frac{1}{f_1} = (n_1 - 1) \left(

Vedclass · Accepted Answer

$\frac{R}{n_1-n_2}$

Vedclass · Answer

(D) For a plano-convex lens with refractive index $n_1$,the focal length $f_1$ is given by the lens maker's formula: $\frac{1}{f_1} = (n_1 - 1) \left( \frac{1}{R} - \frac{1}{\infty} \right) = \frac{n_1 - 1}{R}$.For a plano-concave lens with refractive index $n_2$,the focal length $f_2$ is given by: $\frac{1}{f_2} = (n_2 - 1) \left( -\frac{1}{R} - \frac{1}{\infty} \right) = -\frac{n_2 - 1}{R}$.When these two lenses are combined,the effective focal length $F$ is given by $\frac{1}{F} = \frac{1}{f_1} + \frac{1}{f_2}$.Substituting the values: $\frac{1}{F} = \frac{n_1 - 1}{R} - \frac{n_2 - 1}{R} = \frac{n_1 - 1 - n_2 + 1}{R} = \frac{n_1 - n_2}{R}$.Therefore,the focal length of the combination is $F = \frac{R}{n_1 - n_2}$.

$A$ plano-convex lens fits exactly into a plano-concave lens. Their plane surfaces are parallel to each other. The lenses are made of different materials with refractive indices $n_1$ and $n_2$,and $R$ is the radius of curvature of the curved surfaces. What is the focal length of the combination?

Similar Questions

Two lenses of power $6D$ and $-2D$ are combined to form a single lens. The focal length of this lens will be (in $m$)

Two thin lenses are of same focal lengths $(f)$,but one is convex and the other one is concave. When they are placed in contact with each other,the equivalent focal length of the combination will be:

Two lenses of power $-1.6 D$ and $+2.1 D$ respectively are placed in contact. The focal length of the combination is (in $cm$)

$A$ converging lens of focal length $30 \,cm$ is placed in contact with another converging lens of unknown focal length. Then,the possible value for the focal length of the combination is ......... $cm$.

Two thin lenses of focal lengths $20 \ cm$ and $25 \ cm$ are placed in contact. The effective power of the combination is (in $D$)

Vedclass Test Series

Exam Paper Generator

Online Exam Module