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The power of a lens is $ + 2.5D$. What kind of lens it is and what is its focal length?
(A) $40cm$, Convex lens
(B) $30cm$, Convex lens
(C) $400cm$, Concave lens
(D) $400cm$, Convex lens

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Last updated date: 20th Jun 2024
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Answer
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Hint We can get the focal length of the lens from its power as the focal length is the reciprocal of the power of a lens. And the positive or negative sign of the focal length will tell us about the kind of lens as positive is convex lens and negative is concave lens.
Formula Used: In this solution we will be using the following formula,
$\Rightarrow f = \dfrac{1}{P}$
where $f$ is the focal length of the lens and $P$ is the power of the lens.

Complete step by step answer
For any kind of lens, the power of the lens and the focal length of the lens are related by the formula, $f = \dfrac{1}{P}$
In the question we are given that the power of the lens is $ + 2.5D$.
So we have $P = + 2.5D$. Now we can substitute this value in the formula. So we get,
$\Rightarrow f = \dfrac{1}{{2.5}}$
On calculating this we get,
$\Rightarrow f = 0.4m$
In the options, we are given the answer in centimeters. So on converting we get the value of the focal length of the lens as,
$\Rightarrow f= 0.4 \times 100cm = 40cm$
Now the power of the lens given in question is positive. So as a result the focal length of the lens is also positive.
The positive value of the focal length is present in a convex lens where the concave lens has a negative value of the focal length. So the focal length is $40cm$ and the lens is a convex lens.
Therefore, the correct answer is option D.

Note
The power of a lens denotes the ability of a lens to bend the light that is passing through it. The greater is the power of the lens, the more is the light refracted while passing through it. It is also the reciprocal of the focal length. So the more power of the lens, the less is its focal length. For a convex lens it measures the converging ability and for a concave lens, it measures the diverging ability. The unit of the power of a lens is Diopters and it is denoted by D.