Question

A farsighted eye is corrected by placing a converging lens in front of the eye. The lens will create a virtual image that is located at the near point (the closest an object can be and still be in focus) of the viewer when the object is held at a comfortable distance, usually taken to be 25.0 cm. If a person has a near point of 55.5 cm, what power reading glasses should be prescribed to treat this hyperopia? Assume that the distance from the eye to the lens is negligible.

Answer 1

To correct hyperopia, a lens with a power of 5 diopters should be prescribed to a person with a near point of 55.5 cm.

Step-by-step explanation:

To calculate the power of the eyeglass lens needed to correct hyperopia, we need to know the near point of the person. In this case, the near point is given as 55.5 cm. The power of a lens is measured in diopters (D), which is equal to 1 divided by the focal length in meters. Since the image produced by the lens should be located at the near point, which is farther from the eye than the object, we need to calculate the lens power using the formula: Power of lens (P) = 1 / F, where F is the focal length of the lens.

Given that the near point is 55.5 cm (0.555 m) and the object distance is 25.0 cm (0.250 m), we can use the lens formula to find the focal length: 1 / F = 1 / 0.555 - 1 / 0.250. Solving this equation gives us F = 0.200 m. Now we can calculate the power of the lens: P = 1 / 0.200 = 5 D.

Therefore, a lens with a power of 5 diopters should be prescribed to correct this hyperopia.

Answer 2

To prescribe reading glasses for hyperopia, the power of the converging lens can be calculated using the lens formula, with the virtual image set at the near point when an object is held at a comfortable reading distance. Positive optical power indicates a converging lens to compensate for the farsighted eye that under converges light rays.

Step-by-step explanation:

Farsightedness, or hyperopia, is a condition where the eyes cannot focus on near objects, and this is corrected with the help of a converging lens. To calculate the power of reading glasses needed for a person with a near point of 55.5 cm, when the object is at a comfortable reading distance of 25.0 cm, one must use the lens formula. The lens formula is given by P = 1/f, where P is the power in diopters (D) and f is the focal length in meters.

In this case, you want the virtual image to be at the near point distance of 55.5 cm when the actual object is at 25 cm. This means that the lens must have a focal length (f) such that it brings the object located at 25 cm (0.25 m) into focus at 55.5 cm (0.555 m). Using the lens maker's equation with these values, you can solve for f and then calculate the optical power P required for the person's reading glasses.

Therefore, the focal length (f) for the converging lens is f = 1/(1/object distance - 1/image distance) = 1/(1/0.25 - 1/0.555) meters. After calculating the value of f, you would then calculate the power P = 1/f in diopters. Keep in mind that for a converging lens used to correct hyperopia, the power is expected to be positive, indicating a converging effect.