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Q.

Two lenses have powers $+ 2.5 D$ and $- 0.5 D$ respectively. The focal length of the combination of the two lenses in contact is [[1]] $cm$ .

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Detailed Solution

Two lenses have powers

+ 2.5 D

and

- 0.5 D

respectively. The focal length of the combination of the two lenses in contact is

50 cm

.
Given,
Power of one lens,

P_{1} = + 2.5 D

Power of second lens,

P_{2} = - 0.5 D

The power of a lens is a measure of its degree of convergence or divergence of light rays’ incident on it. Power is the reciprocal of the focal length of the lens. The equivalent power of two lenses is the sum of individual powers.
Equivalent power,

P = P_{1} + P_{2}

\Rightarrow P = + 2.5 D + (- 0.5 D)

\Rightarrow P = 2.5 D - 0.5 D

\Rightarrow P = + 2.0 D

The focal length of combination,

f = \frac{1}{P}

\Rightarrow f = \frac{1}{2}

\Rightarrow f = 0.5 m

\Rightarrow f = 50 cm

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Two lenses have powers +2.5 D and -0.5 D respectively. The focal length of the combination of the two lenses in contact is [[1]] cm.