Question

Ordinary glasses are worn in front of the eye and usually 2.00 cm in front of the eyeball. A certain person can see distant objects well, but his near point is 50.0 cm from his eyes instead of the usual 25.0 cm . Suppose that this person needs ordinary glasses What focal length lenses are needed to correct his vision ?What is their power in diopters?

Answer 1

Answer:

The focal length is 15.549 cm

The power of the lens is 0.0643 D

Solution:

As per the question:

The near point is 50.0 cm

Distance of the glasses from the eyeball, d = 2.00 cm

The near point of a normal human eye is 25 cm

Now,

The image distance, v' = 50.0 - 2.00 = 48.0 cm

The object distance, u' = 25.0 - 2.00 = 23.0 cm

Now, using the Lens maker formula to calculate the focal length:

$\frac{1}{f} = \frac{1}{u'} + \frac{1}{v'}$

$\frac{1}{f} = \frac{1}{48.0} + \frac{1}{23.0} = 0.0643$

f = 15.549 cm

Now, the power of the lens in diopters is given by:

$P = \frac{1}{f} = \frac{1}{15.549} = 0.0643 D$