Optics problem (myopia, glasses)

In summary, a person with myopia and glasses with a correction of -1.75 diopters will be able to see themselves clearly in a mirror 50 cm away. The formula 1/f = 1/v + 1/b can be used to calculate the object distance (b) which in this case is 26 cm. However, if the object distance is defined as the distance from the eye lens to the virtual object, then it should be 100 cm. This is because the net effect of the eye lens and negative spectacle lens must result in a positive focal length for the viewer to see a clear image on their retina. Therefore, the correct formula for focusing on a virtual object at p = 1m is
  • #1
tomkoolen
40
1
A person with myopia is standing 50 cm in front of a mirror with glasses on (-1.75 dpt). Will he be able to see himself clearly?



1/f = 1/v + 1/b



I get that b = 26 cm. However my teacher says it should be 100. Is this correct?
 
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  • #2
tomkoolen said:
A person with myopia is standing 50 cm in front of a mirror with glasses on (-1.75 dpt). Will he be able to see himself clearly?



1/f = 1/v + 1/b



I get that b = 26 cm. However my teacher says it should be 100. Is this correct?

Trick question! Remember that his glasses correct to give a sharp image at infinity, whatever the strength of the glasses happen to be.
 
  • #3
If b stands for the object distance, 100cm is clearly correct. If you disagree, by what argument? If b is something else, what is it?
 
  • #4
haruspex said:
If b stands for the object distance, 100cm is clearly correct. If you disagree, by what argument? If b is something else, what is it?

Come to think of it, neither the OP nor his teacher, nor I for that matter, answered the question, which is a bit vague to begin with.

Presumably, his spectacles enable him to see clearly at infinity. If he still enjoys power of accommodation, he can shorten the focal length of his eye lens to focus an object at 1m to the focal point on his retina. An older person would not necessarily be able to do that.

A myopic person has image distance (distance betw. his eye lens and retina) too short so he needs a diverging lens to focus infinity on his retina. Trying to use 1/f = 1/p + 1/q is tricky because the separation of his eye lens and his spectacle lens consitutes a "thick" lens with undefined image distance q, depending on how he wears his glasses.
 
  • #5
Alright thank you very much! I now get:

-1.75 = 1/1 + 1/b (you guys call it q)
then b does not equal 1, however the teacher says it does. Could you explain this?
 
  • #6
tomkoolen said:
Alright thank you very much! I now get:

-1.75 = 1/1 + 1/b (you guys call it q)
then b does not equal 1, however the teacher says it does. Could you explain this?

This formula is meaningless. Your b is a negative number!

You are ignorig the eye lens. q is the effective image distance. The net effect of the eye lens plus the negative spectacle lens must still be a positive focal length, otherwise you don't get a real image on the retina.

As I've said before, the -1.75 diopter number has no significance by itself. It's just the correction the viewer needs to get a sharp image at infinity. Then, to see an object at a distance of p = 1m he needs to squeeze his eye lens down, thereby decreasing its focal length, so that the divergent rays from the virtual object in the mirror are again in sharp focus on his retina.

It can be shown that, if you stack two lenses of focal lengths f1 and f2 close together that the effective focal length f of the combined lens is given by 1/f = 1/f1 + 1/f2.
So if f1 = focal length of eye lens (about 1 cm?) and 1/f2 = -1.75 m-1, the right formula for focusing on a virtual object at p = 1m becomes 1/f = 1/p + 1/q where f and q ~ 0.01m, p = 1m, and q represents the (reduced) q of a myoptic eye. f is now the combination spectacle lens and his squeezed-down eye lens.

In any case, it should be obvious that p = 1m; it's just twice the distance from the eye to the mirror.
 

1. What is myopia and how does it affect vision?

Myopia, also known as nearsightedness, is a common vision condition in which objects up close appear clear, but objects far away appear blurry. This is because the eyeball is too long or the cornea is too curved, causing the light to focus in front of the retina instead of directly on it. This results in difficulty seeing distant objects clearly without corrective lenses.

2. How do glasses correct myopia?

Glasses for myopia have concave lenses that help to diverge light rays before they enter the eye, allowing them to focus correctly on the retina. This helps to correct the refractive error and improve distance vision. The strength of the lenses needed depends on the severity of the myopia.

3. Can myopia be prevented?

There is currently no proven way to prevent myopia from developing, but there are some studies that suggest spending more time outdoors and reducing screen time may help to delay the onset or slow the progression of myopia in children.

4. Are there any risks associated with wearing glasses for myopia?

Wearing glasses for myopia does not pose any significant risks. However, some people may experience side effects such as headaches or eye strain when they first start wearing glasses, which usually subside as the eyes adjust to the new correction.

5. Can myopia be treated permanently?

There are several treatments available for myopia, such as LASIK surgery and orthokeratology, that can provide a more permanent solution. However, these treatments are not suitable for everyone and should be discussed with an eye doctor to determine the best course of action for each individual case.

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