Question

1. You wish to produce upright virtual images of an object with the given magnifications using a diverging

lens. Where must you place the object in each case (express your answer in terms of the focal length of

the lens)? (a) M = 0.5 (b) M = 0.75

A person with a normal lens-to-retina distance wears contact lenses with an optical power of 1.54 D in

order to be able to clearly see objects 20 cm in front of them. (a) What kind of vision defect does this person

have? (b) What is this person’s near point (without the contact lenses)?


Kindly explain in detail and give the correct solution.

Answer 1

1) The magnification of a diverging lens is

$$M=\frac{f}{f-o},\\\space\\ o=\frac{f(M-1)}{M}.$$

Depending on the focal length (keep in mind it's negative), you can find the position of the object.

2) (a) Since the optical power is positive, it is farsightedness.

(b) The near point is

$$o=\frac{1}{D}=\frac{1}{1.54}=0.65\text{ m}.$$