A short-sighted person can see objects most distinctly at a distance of 16 cm. If he wears spectacles at a distance of 1 cm from the eye, what focal length should they have so as to enable him to see distinctly at a distance of 26 cm?

Solution

The person is suffering from myopia (shortsightedness) and wears spectacles at a distance of 1 cm from the eyes.
Therefore,
Image is formed at a distance,

v = - (16 - 1) = 15 c m

Also given,
Object distance,

u = - (26 - 1) cm = - 25 cm

Using len's formula,

\frac{1}{f} = \frac{1}{v} - \frac{1}{u} = \frac{1}{- 15} - \frac{1}{- 25}

= \frac{1}{25} - \frac{1}{15} = - \frac{2}{75}

f = - \frac{75}{2} cm = - 37.5 cm

Focal length is nagative. So, a concave lens of focal length 37.5 cm is to be used.

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Wave Optics

A short-sighted person can see objects most distinctly at a distance of 16 cm. If he wears spectacles at a distance of 1 cm from the eye, what focal length should they have so as to enable him to see distinctly at a distance of 26 cm?

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