How Can We Determine if Someone is Farsighted?

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In summary, the correct answer to the question about the characteristic of a farsighted person is A: the minimum focal length they can get for the lens of their eye is not small enough. This is determined by the equation 1/f = 1/p + 1/q, where f is the focal length, p is the object distance, and q is the image distance. The professor's explanation for this answer was incorrect, as small p requires small f, and if the objects appear blurry, it is because the minimum focal length for the lens of the eye is not small enough.
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Homework Statement


Which of the following is a characteristic of a farsighted person (nearby objects appear blurry)?
a)the minimum focal length they can get for the lens of their eye is not small enough.
b) the maximum focal length they can get for the lens of their eye is not large enough
c) their lens of their eye is not symmetrical

Homework Equations


1/f = 1/p + 1/q

f = 1/(1/p + 1/q)

p = 1/(1/f-1/q)

f is focal length, p is object distance, q is image distance

The Attempt at a Solution



The answer is B. I agree, but I don't understand my professor's explanation.

The explanation for B being correct:
"with q fixed, then to make p small f --> large. If can't get f --> large then can't get p --> small."

My reasoning - I found that when P increases, F must increase, which is the opposite of the explanation. If when P decreases F decreases, and if when P is small the objects are blurry, F must be too small.

If someone can confirm or deny the validity of my reasoning and explain the explanation given by my professor it would be much appreciated.
 
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  • #2
The correct answer is A.

Your professor made a mistake, maybe?
 
  • #3
dauto said:
The correct answer is A.

Your professor made a mistake, maybe?

He certainly may be wrong, though it is unlikely. Where is the flaw in my reasoning?
 
  • #4
You said it yourself. You got the opposite effect as the one used in the explanation. Small p requires small f. If it's blurry it's because they couldn't produce such a small f because "the minimum focal length they can get for the lens of their eye is not small enough". Notice how I concluded the logical statement with the quoted answer from item A. A is the correct answer.
 
  • #5
dauto said:
You said it yourself. You got the opposite effect as the one used in the explanation. Small p requires small f. If it's blurry it's because they couldn't produce such a small f because "the minimum focal length they can get for the lens of their eye is not small enough". Notice how I concluded the logical statement with the quoted answer from item A. A is the correct answer.

Ah, you are right. I confused myself. It's clear now. Thanks!
 

FAQ: How Can We Determine if Someone is Farsighted?

What is the difference between convex and concave lenses?

The main difference between convex and concave lenses is their shape. Convex lenses bulge outwards and are thicker in the middle, while concave lenses are thinner in the middle and bulge inwards. This shape difference causes them to have different optical properties, as convex lenses converge light and concave lenses diverge light.

How do lenses correct vision problems?

Lenses correct vision problems by refracting (bending) light as it passes through the lens and into the eye. This refraction helps to focus the light onto the retina in the back of the eye, allowing for clearer vision. For nearsightedness, a concave lens is used to diverge light before it enters the eye, while for farsightedness, a convex lens is used to converge light.

What is the difference between a converging and a diverging lens?

A converging lens is a convex lens that causes light rays to bend towards each other and come together at a focal point, while a diverging lens is a concave lens that causes light rays to spread out and not converge at a focal point. This difference in light bending abilities is what makes these lenses useful for correcting different types of vision problems.

How do lenses affect the appearance of objects?

Lenses can affect the appearance of objects in several ways. Convex lenses can magnify objects, making them appear larger than they actually are. Concave lenses can have the opposite effect, making objects appear smaller. Lenses can also affect the shape of objects, as light is bent and distorted as it passes through the lens.

What are some common uses for lenses in everyday life?

Lenses have many everyday uses, including correcting vision problems with glasses or contact lenses, magnifying objects with a microscope or telescope, and taking photos with cameras. Lenses are also used in many optical instruments, such as binoculars and projectors. In addition, lenses are used in various industries, such as in the production of precision tools and equipment.

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