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

The prescription for glasses needed to correct the person's farsightedness should have lenses with a power of approximately 4.35 diopters.

Step-by-step explanation:

To correct the vision of a person with a near point of 50.0 cm, we must find a lens that will allow them to clearly see objects at the normal near point of 25.0 cm. First, we calculate the lens's focal length (f), which is the distance at which it would bring parallel rays to focus. The formula for lens power (P) in diopters (D) is given by P = 1/f (in meters). The needed focal length is the new near point (25.0 cm, or 0.25 m) minus the distance the glasses are from the eye (2.00 cm, or 0.02 m). Thus, the focal length is f = 0.25 m - 0.02 m = 0.23 m. After conversion to meters, calculating the power gives P = 1/0.23 m ≈ 4.35 D.

The prescription for the glasses should therefore have lenses with a power of approximately 4.35 diopters to correct the vision to a normal near point.

Answer 2

Focal length: 44.16cm, Power: 2.2645 diopters

Step-by-step explanation:

The object and image locations are the distance from the point to the lens.

object location = 25 - 2 = 23cm

image location = 50 - 2 = -48cm

the image location is negative since the image is virtual (the light rays do not pass through the image)

We can then use the lens equation to find the focal length.

1/object location + 1/image location = 1/focal length

(1/23)-(1/48)=1/f

Focal length = 44.16cm

To find the power we use the equation

D=1/f where f is the focal length in meters

44.16cm = 0.4416m

power = 2.2645 diopters