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Wave Optics

Question

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

Solution

Given,
Object distance, u = -25 cm
Image distance, v = -50 cm
Focal length, f = ?

Now, using lens formula,

\frac{1}{f} = \frac{1}{v} - \frac{1}{u} = \frac{1}{- 50} - \frac{1}{- 25} = - \frac{1}{50} + \frac{1}{25}

= \frac{- 1 + 2}{50} = \frac{1}{50}

∴

f = 50 cm .

Power of the lens,

P = \frac{1}{f (in m)} = \frac{100}{f (in cm)}

\Rightarrow

P = \frac{100}{50} = + 2 D

Hence, the corrective lens is convex because, power of the lens is positive.

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