What is the size of the image of a tree on a man's retina?

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In summary, the man is looking at a tree of height 20.0m a distance of 300m away. The cornea has a radius of curvature of 7.7mm, the eye has a refractive index of 1.47, and the length of the eye is 24.0mm. By using the equation M=-di/do=hi/ho and assigning values for di, do, and ho, we can solve for the height of the image, which is our one unknown.
  • #1
anotherperson
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Homework Statement


A man looks at a tree of height 20.0m a distance of 300m away. the cornea has a radius of curvature of 7.7mm, eye has refractive index of 1.47 and the length of the eye is 24.0mm.

Calculate the size of the image of the tree on the man's retina.


Homework Equations


n1/p+n2/q=n2-n2/R


The Attempt at a Solution


i tired the following but i don't think it is correct
n1=1.47
n2=1.0
R=7.7
p=20

1.47/20+1.0/q=1.47-1.0/7.7
=0.06
 
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  • #3
but i don't know the focal length...
 
  • #4
You don't need it at all. I strongly suspect that at least 2 pieces of given information are extraneous, maybe more. Try this equation, relating magnification, M, to distances and height to the image and object.

[tex]M=-\frac{d_{i}}{d_{o}}=\frac{h_{i}}{h_{o}}[/tex]
 
  • #5
so if i use these values (changing the units of course) is this correct
di=7.7mm
do=300m
hi=24.0mm
ho=20.0m
and then using the magnification i get i can work out the size of the tree?
 
  • #6
Well, since the image is formed on the back of the eye, di=24.0mm, the length of the eye. Remember that you are trying to solve for the height of the image, hi. This is your one unknown. Your do and ho look fine.
 

1. What is the function of the lens in the eye?

The lens in the eye helps to focus light rays onto the retina, which then sends visual information to the brain. This allows us to see objects clearly at different distances.

2. How does the lens change shape to focus on objects at different distances?

The lens is elastic and can change shape through a process called accommodation. When we look at distant objects, the lens becomes flatter, and when we look at closer objects, the lens becomes more rounded.

3. Can the lens become damaged or diseased?

Yes, the lens can become damaged or diseased, leading to conditions such as cataracts, where the lens becomes cloudy, or presbyopia, where the lens loses its elasticity and makes it difficult to focus on close objects.

4. Are there different types of lenses in the eye?

Yes, there are two types of lenses in the eye: the crystalline lens and the cornea. The crystalline lens is located behind the iris and helps with accommodation, while the cornea is the clear outer layer of the eye that also helps to focus light.

5. Can we improve our vision through the use of corrective lenses?

Yes, corrective lenses, such as glasses or contact lenses, can help to improve vision by compensating for any refractive errors in the eye, such as nearsightedness or farsightedness. Surgery, such as LASIK, can also correct these refractive errors by reshaping the cornea.

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