Question

an older person needs a pair of reading glasses.Her near point is at 48 cm from her eyes and reading glasses are 2 cm from her eyes. The glasses should allow her to read 25 cm away. What are the object and image distances? what is the magnification of these lenses? What is the focal length of the pair of glasses? What is the optical power of the lens pair? What type of lenses (converging, diverging) does she need?

Answer 1

The object is at 25cm from her eyes which means that it is at a distance of 25 - 2 = 23 cm from the lens

So, object distance is 23 cm. In cartesian coordinate system u = -23 cm

Image is at 48 cm from her eyes, which means it is at 48 - 2 = 46 cm from the lens.

So, image distance = 46 cm In cartesian coordinate system v = - 46 cm

Using the lens formula, 1/f = 1/v - 1/u

1/f = 1/-46 - 1/-23 = 0.02173913

f = 46 cm = 0.46 m

Magnification m = v/u = -46 / -23 = 2

Power = 1/.46 = 2.1739 diopters

Focal length is positve, so converging lens are used.