JEE Advanced 2014 · Paper 2 · Physics Q18 · Dronacharya Exams

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PhysicsList match+3 / -1Question 18 of 60

Four combinations of two thin lenses are given in List I. The radius of curvature of all curved surfaces is $r$ and the refractive index of all the lenses is 1.5. Match lens combinations in List I with their focal length in List II and select the correct answer using the code given below the lists.

Two identical equiconvex (biconvex) thin lenses placed in contact.

Two plano-convex lenses with flat faces outward and convex faces facing each other, touching at the centre.

Two plano-concave lenses with flat faces outward and concave faces facing each other, enclosing a biconvex gap (outline is a rectangle with a lens-shaped space inside).

An equiconvex (biconvex) lens in contact with a plano-concave lens whose concave face fits against it.

List I

P
Q
R
S

List II

1
$2r$
2
$r/2$
3
$-r$
4
$r$

A

P → 1; Q → 2; R → 3; S → 4

B

P → 2; Q → 4; R → 3; S → 1

C

P → 4; Q → 1; R → 2; S → 3

D

P → 2; Q → 1; R → 3; S → 4

Answer and worked solution

Official answer: B

Single lenses ( $\mu=1.5$ , all radii $r$ ), by the lens-maker's formula $\frac1f=(\mu-1)\left(\frac1{R_1}-\frac1{R_2}\right)$ :

equiconvex: $\frac1f=\frac{0.5\times2}r$ , $f=r$ ;
plano-convex: $f=2r$ ;
plano-concave: $f=-2r$ .

Combinations in contact ( $\frac1F=\frac1{f_1}+\frac1{f_2}$ ):

P two equiconvex: $\frac2r$ , $F=\frac r2$ → 2.
Q two plano-convex: $\frac1{2r}+\frac1{2r}$ , $F=r$ → 4.
R two plano-concave: $F=-r$ → 3.
S equiconvex + plano-concave: $\frac1r-\frac1{2r}=\frac1{2r}$ , $F=2r$ → 1.

(B) P → 2, Q → 4, R → 3, S → 1

Topics:Combination of lenses and mirrors Thin lenses and lens maker's formula

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