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The near point of a hypermetropic person is $50 cm$ from the eye. Which of the following is correct for the power of the lens required to enable the person to read clearly a book held at $25 cm$ from the eye?

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3 D

2 D

2.5 D

3.2 D

answer is B.

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Detailed Solution

The power of the lens required is

2 D

.
Given,
Image distance,

v = - 50 cm

and object distance,

u = - 25 cm

.
Form the lens formula,

\frac{1}{f} = \frac{1}{v} - \frac{1}{u}

Where

f

v

, and

u

are the focal length, image distance, and object distance, respectively.
On substituting the given values, we get the focal length as

\Rightarrow \frac{1}{f} = \frac{1}{- 50} - \frac{1}{(- 25)}

\Rightarrow \frac{1}{f} = \frac{1}{50}

\Rightarrow f = 50 cm

Hence, the focal length is

50 cm

.
It is known that the power of a lens is the reciprocal of the focal length of the lens. Mathematically,

P = \frac{100}{f}

Where

f

is the focal length of the lens in centimetres.
On substituting the given values, we get the power as

\Rightarrow P = \frac{100}{50}

\Rightarrow P = 2 D

Hence, the required power of the lens is

2 D

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