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A concave lens of focal length 25 cm and...

A concave lens of focal length 25 cm and a convex lens of focal length 20 cm are placed in contact with each other. What is the power of this combination ? Also, calculate focal length of the combination.

A

`0.5D` , `10cm`

B

`1D` , `100cm`

C

`-1D` , `100cm`

D

`1.5D` , `50cm`

Text Solution

Verified by Experts

The correct Answer is:
B
Here, focal length of concave lens, `f_(1) = -25 cm`, focal length of convex lens, `f_(2) = + 20 cm`
power of the combination, `P = ?`, focal length of the combination, `F = ?`
Clearly, `P_(1) = 100/(f_(1)(cm)), P = 100/(-25) = -4` dioptre and `P_(2) = 100/(f_(2)(cm)) = 100/20 = + 5` dioptre
As `P = P_(1) + P_(2), P = - 4 + 5 = 1` dioptre
Thus, `F = 100/P = 100 cm = 1 m`.
Positive sign of P and F indicates that the combination of two given lenses behaves as a convex lens.
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