SATHEE: Optics 3 Question 1

Optics 3 Question 1

1. One plano-convex and one plano-concave lens of same radius of curvature $R$ but of different materials are joined side by side as shown in the figure. If the refractive index of the material of 1 is $μ_{1}$ and that of 2 is $μ_{2}$ , then the focal length of the combination is

(2019 Main, 10 April I)

(a) $\frac{2 R}{μ_{1} - μ_{2}}$

(b) $\frac{R}{2 - (μ_{1} - μ_{2})}$

(d) $\frac{R}{μ_{1} - μ_{2}}$

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Answer:

Correct Answer: 1. (d)

Solution:

Focal length of a lens is given as

$\frac{1}{f} = (μ_{1} - 1) \frac{1}{R_{1}} - \frac{1}{R_{2}}$

$∴$ Focal length of plano-convex lens, i.e. lens 1,

$R_{1} = \infty and R = - R$

$\begin{aligned} \Rightarrow \frac{1}{f_{1}} = \frac{μ_{1} - 1}{R} \\ or f_{1} = \frac{R}{(μ_{1} - 1)} \end{aligned}$

Similarly, focal length of plano-concave lens, i.e. lens 2,

$R_{1} = - R and R_{2} = \infty$

$\begin{aligned} \Rightarrow \frac{1}{f_{2}} = - \frac{(μ_{2} - 1)}{R} \\ or f_{2} = \frac{- R}{(μ_{2} - 1)} \end{aligned}$

From Eqs. (i) and (ii), net focal length is

$\begin{aligned} \frac{1}{f} & = \frac{μ_{1} - 1}{R} - \frac{μ_{2} - 1}{R} = \frac{μ_{1} - μ_{2}}{R} \\ \Rightarrow f & = \frac{R}{μ_{1} - μ_{2}} \end{aligned}$

Optics 3 Question 1

1. One plano-convex and one plano-concave lens of same radius of curvature $R$ but of different materials are joined side by side as shown in the figure. If the refractive index of the material of 1 is $μ_{1}$ and that of 2 is $μ_{2}$ , then the focal length of the combination is

Answer:

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Optics 3 Question 1

1. One plano-convex and one plano-concave lens of same radius of curvature R but of different materials are joined side by side as shown in the figure. If the refractive index of the material of 1 is μ1 and that of 2 is μ2, then the focal length of the combination is

Answer:

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

NCERT Exercise Video Solution

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1. One plano-convex and one plano-concave lens of same radius of curvature $R$ but of different materials are joined side by side as shown in the figure. If the refractive index of the material of 1 is $μ_{1}$ and that of 2 is $μ_{2}$ , then the focal length of the combination is