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Geometrical Optics question

2025 · 24 Jan · Shift 1 · Q65
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Geometrical Optics question

2025 · 24 Jan · Shift 1 · Q65

JEE MainPhysicsGeometrical OpticsMCQ+4 / −1
A plano-convex lens having radius of curvature of first surface 2 cm exhibits focal length of f1f_1f1​ in air. Another plano-convex lens with first surface radius of curvature 3 cm has focal length of f2f_2f2​ when it is immersed in a liquid of refractive index 1.2. If both the lenses are made of same glass of refractive index 1.5 , the ratio of f1f_1f1​ and f2f_2f2​ will be
  1. A
    2:32: 32:3
  2. B
    1:31: 31:3
  3. C
    1:21: 21:2
  4. D
    3:53: 53:5
View written solutionFree

Correct answer: B

  1. Use lens maker formula

For a thin lens in a medium of refractive index nmn_mnm​:

1f=(nℓnm−1)(1R1−1R2)\frac{1}{f} = \left(\frac{n_\ell}{n_m}-1\right)\left(\frac{1}{R_1}-\frac{1}{R_2}\right)f1​=(nm​nℓ​​−1)(R1​1​−R2​1​)

where nℓn_\ellnℓ​ is refractive index of lens material.

For a plano-convex lens, one surface is plane, so its radius is ∞\infty∞.

Thus,

(1R1−1R2)\left(\frac{1}{R_1}-\frac{1}{R_2}\right)(R1​1​−R2​1​)

will reduce to just the curved surface contribution in magnitude.

  1. First lens in air

Given:

  • nℓ=1.5n_\ell = 1.5nℓ​=1.5
  • nm=1n_m = 1nm​=1 (air)
  • curved surface radius R=2 cmR = 2\text{ cm}R=2 cm

So,

1f1=(1.51−1)(12)=(0.5)(12)=14\frac{1}{f_1} = \left(\frac{1.5}{1}-1\right)\left(\frac{1}{2}\right) = (0.5)\left(\frac{1}{2}\right)=\frac{1}{4}f1​1​=(11.5​−1)(21​)=(0.5)(21​)=41​

Hence,

f1=4 cmf_1 = 4\text{ cm}f1​=4 cm
  1. Second lens immersed in liquid

Given:

  • nℓ=1.5n_\ell = 1.5nℓ​=1.5
  • nm=1.2n_m = 1.2nm​=1.2
  • curved surface radius R=3 cmR = 3\text{ cm}R=3 cm

Relative refractive index of lens w.r.t. liquid:

nℓnm=1.51.2=1.25\frac{n_\ell}{n_m} = \frac{1.5}{1.2} = 1.25nm​nℓ​​=1.21.5​=1.25

Therefore,

1f2=(1.25−1)(13)=0.25⋅13=112\frac{1}{f_2} = (1.25-1)\left(\frac{1}{3}\right) = 0.25\cdot \frac{1}{3} = \frac{1}{12}f2​1​=(1.25−1)(31​)=0.25⋅31​=121​

So,

f2=12 cmf_2 = 12\text{ cm}f2​=12 cm
  1. Find the ratio
f1:f2=4:12=1:3f_1:f_2 = 4:12 = 1:3f1​:f2​=4:12=1:3
  1. Check options
  • A: 2:32:32:3 ❌
  • B: 1:31:31:3 ✅
  • C: 1:21:21:2 ❌
  • D: 3:53:53:5 ❌

So the correct option is B.

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