Answer:
Option (D) 1.778 diopters
Given:
Near point of a person = 45 cm
Solution:
To calculate the prescription's lens power of the person:
Near point for a normal human eye = 25 cm
So, object distance, u = 25 cm
For an object to be clearly seen by the person, the image formation should be at his near point i.e., 45 cm and the image formed will be virtual in nature.
Therefore,
image distance, v = - 45 cm (since, the image formed is virtual and behind the mirror)
Now, using lens maker's formula:
[tex]\frac{1}{f} = \frac{1}{u} + \frac{1}{v}[/tex]
where
f = focal length
Putting the values of u and v in the above formula, we get:
[tex]\frac{1}{f} = \frac{1}{25} - \frac{1}{45}[/tex]
f = 56.24 cm 0.5624
Now, power is the reciprocal of focal length and is given by:
Power, P = [tex]\frac{1}{f}[/tex]
P = [tex]\frac{1}{0.5624}[/tex]
P = 1.778 diopters
