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Geometrical Optics question

2007 · Shift 0 · Q68
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Geometrical Optics question

2007 · Shift 0 · Q68

JEE MainPhysicsGeometrical OpticsMCQ+4 / −1
Two lenses of power −15D-15D−15D and +5D+5D+5D are in contact with each other. The focal length of the combination is
  1. A
    +10 cm+ 10\,cm+10cm
  2. B
    −20 cm- 20\,cm−20cm
  3. C
    −10 cm- 10\,cm−10cm
  4. D
    +20 cm+ 20\,cm+20cm
View written solutionFree

Correct answer: C

  1. Use the formula for lenses in contact

For two thin lenses in contact, the powers add:

Peq=P1+P2P_{\text{eq}} = P_1 + P_2Peq​=P1​+P2​

Given:

P1=−15 D,P2=+5 DP_1 = -15\,D, \qquad P_2 = +5\,DP1​=−15D,P2​=+5D

So,

Peq=−15+5=−10 DP_{\text{eq}} = -15 + 5 = -10\,DPeq​=−15+5=−10D

  1. Relate power and focal length

Power of a lens is

P=1fP = \frac{1}{f}P=f1​

where fff is in meters.

Thus,

f=1Peq=1−10 m=−0.1 mf = \frac{1}{P_{\text{eq}}} = \frac{1}{-10} \, m = -0.1\,mf=Peq​1​=−101​m=−0.1m

  1. Convert into centimeters

−0.1 m=−10 cm-0.1\,m = -10\,cm−0.1m=−10cm

  1. Match with the options

So the focal length of the combination is

−10 cm\boxed{-10\,cm}−10cm​

This corresponds to Option C.

  1. Comparison with stored correct answer

Stored correct answer: C

My derived answer: C

They match.

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