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Geometrical Optics question

2024 · 4 Apr · Shift 1 · Q64
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Geometrical Optics question

2024 · 4 Apr · Shift 1 · Q64

JEE MainPhysicsGeometrical OpticsMCQ+4 / −1
An effective power of a combination of 5 identical convex lenses which are kept in contact along the principal axis is 25D25 \mathrm{D}25D. Focal length of each of the convex lens is:
  1. A
    50 cm
  2. B
    20 cm
  3. C
    25 cm
  4. D
    500 cm
View written solutionFree

Correct answer: B

  1. Use power addition for lenses in contact

For thin lenses kept in contact, their powers add:

Ptotal=P1+P2+P3+P4+P5P_{\text{total}} = P_1 + P_2 + P_3 + P_4 + P_5Ptotal​=P1​+P2​+P3​+P4​+P5​

Since all 5 lenses are identical, let the power of each lens be PPP. Then,

5P=25 D5P = 25\,\text{D}5P=25D

  1. Find power of each lens

P=255=5 DP = \frac{25}{5} = 5\,\text{D}P=525​=5D

  1. Use relation between power and focal length

P=1fP = \frac{1}{f}P=f1​

where fff is in metres. So,

f=1P=15 m=0.2 mf = \frac{1}{P} = \frac{1}{5}\,\text{m} = 0.2\,\text{m}f=P1​=51​m=0.2m

  1. Convert into cm

0.2 m=20 cm0.2\,\text{m} = 20\,\text{cm}0.2m=20cm

  1. Match with options

The focal length of each convex lens is:

20 cm\boxed{20\,\text{cm}}20cm​

So the correct option is B.

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