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Is it true that a lens of power $+ 2 D$ and lens of power $- 1 D$ are placed in close contact with each other. The combination will behave like a converging lens of focal length $100 cm$ ?

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True

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Detailed Solution

The above statement is true.
A lens of power

+ 2 D

and lens of power

- 1 D

are placed in close contact with each other. The combination will behave like a converging lens of focal length 100 cm.
Given that power

P_{1} = + 2 D

and,
Power

P_{2} = - 1 D

Now,

P = P_{1} + P_{2}

\Rightarrow P = + 2 - 1

(after putting the values of

P_{1}

and

P_{2}

)

\Rightarrow

P = + 1 diopter

since net power is positive , hence the combination will behave as a convex lens.

F = \frac{1}{P}

(

F

is focal length of lens )

\Rightarrow

F = \frac{1}{1 m}

\Rightarrow F = 100 cm

So the combination will behave like a converging lens of focal length

100 cm

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