Optics 3 Question 5

5. A plano-convex lens (focal length f2, refractive index μ2, radius of curvature R ) fits exactly into a plano-concave lens (focal length f1, refractive index μ1, radius of curvature R ). Their plane surfaces are parallel to each other. Then, the focal length of the combination will be

(2019 Main, 12 Jan II)

(a) f1f2

(b) Rμ2μ1

(c) f1+f2

(d) 2f1f2f1+f2

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Answer:

Correct Answer: 5. (c)

Solution:

  1. Given combination is as shown below

As lenses are in contact, equivalent focal length of combination is

1feq=1f1+1f2

Using lens Maker’s formula,

1f=(μ1)1R11R2 Here, 1f1=(μ11)1R1=(1μ1)R and 1f2=(μ21)11R=(μ21)R1feq=μ21R+1μ1R=μ21+1μ1R=μ2μ1R

So, feq=Rμ2μ1.



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