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A convex lens of focal length 20cm is in contact with a concave lens of focal length 10cm. The power of the combination of these lenses is:
1. -5D
2. -10D
3. 10D
4. 5D

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Correct Answer - Option 1 : -5D

Concept:

  • Power of Lens (P): Power of Lens is the reciprocal of focal length (f). 

\(P = \frac{1}{f}\)

  • Unit of Power of Lens is diopter (D).
  • Power of lens signifies, the converging or diverging capability.
  • When two or more lenses are kept in Contact, then the power of the combination of the lens is the sum of the Power of all lenses.

Power of n number of the lens in contact is given as

P = P1 + P2 + P3 + ... Pn

  • Power and focal length of the concave lens are negative.
  • Power and focal length of the convex lens are positive.

​Calculation:

Focal length of (convex) lens 1 f1 = + 20 cm = 0.2 m

Power of lens 1 

\(P_1 = \frac{1}{0.2} = 5 D\) -- (1)

Focal length of (concave) lens 2 f1 = - 10 cm = - 0.1 m 

Power 

\(P_2 = \frac{1}{0.1} = - 10 D\) -- (2)

Power of combination

P = P1 + P2 

⇒ P = 5 D - 10 D (From Eq 1 and 2)

So, the power is - 5 D

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