A person has a near point at 100 cm . What power of lens is required to read at 20 cm if they use spectacles having glasses 2.0 cm separated from the eyes?

Step-by-step solution

The object is to be placed at a distance of 20 cm from the eye. Since the spectacles are 2.0 cm away from the eyes, the object distance from the lens is: u = -(20 - 2.0) = -18 cm The image must be formed at the near point of the person, which is 100 cm from the eye. The image distance from the lens is: v = -(100 - 2.0) = -98 cm Using the lens formula: 1 f = 1 v - 1 u 1 f = 1 -98 - 1 -18 1 f = 1 18 - 1 98 The power of the lens P is given by P = 100 f (where f is in cm): P = 100 18 - 100 98 P = 5.55 - 1.02 = +4.53 D