Question

A nearsighted person can see clearly only objects within 6 feet of her eye. To see distant objects, she should wear eyeglasses of what type and focal length?

A.diverging, 2.8 m
B.diverging, 1.4 m
C.converging, 2.8 m
D.converging, 1.4 m
E.diverging, 0.72 m

Answer 1

A nearsighted person who can only see objects clearly up to 6 feet away needs glasses with diverging lenses. There's no exact match among the given options, but option E (diverging, 0.72 m) is closest to the calculated requirement given the lack of an exact fit.

Step-by-step explanation:

A nearsighted person who can see clearly only objects within 6 feet (approximately 1.83 meters) of her eye has a condition called myopia.

This means that the eye focuses light in front of the retina, making distant objects appear blurry.

To correct this condition, she needs glasses with diverging lenses, which will spread out the light rays before they enter the eye so that they can be focused on the retina.

To determine the appropriate focal length for the glasses, we use the lensmaker's formula: Power (P) = 1/focal length (f), with P in diopters (D) and f in meters. Since her clear vision is limited to 6 feet, her far point is 6 feet or 1.83 meters.

Assuming that the glasses would allow her to see at infinity (far point of normal vision), the power required would be P = 1/1.83 meters, which is approximately -0.55 D.

Among the options provided, option E, a diverging lens with a focal length of 0.72 meters (which corresponds to a power of -1.39 D), is closest to what would be required to correct her vision to see distant objects clearly.

Answer 2

A nearsighted person who can see clearly up to 6 feet would need a pair of glasses with diverging lenses. None of the focal lengths provided in the question options exactly match the conversion of 6 feet to meters (1.83m). For the provided options, the closest focal length is likely intended to be the correct answer, which would be option E, diverging with 0.72 m focal length.

Step-by-step explanation:

A person who is nearsighted, or has myopia, can see objects clearly only when they are close to their eyes. To see distant objects clearly, the person requires diverging lenses because they spread out light rays before they enter the eye. This helps in reducing the eye's lens overconvergence so that the image can be focused correctly on the retina. The focal length of the lens can be calculated using the formula 1/f = 1/do + 1/di, where do is the object distance (infinity for distant objects), and di is the image distance, equal to the far point of the nearsighted person. For a person who can see clearly up to 6 feet (approximately 1.83 meters), the focal length would be negative because it's a diverging lens. The question provides options with different focal lengths in meters. Thus, the correct option is one with a diverging lens, with a focal length that accounts for a far point of 6 feet.