Range of Powers of Eye Lens - Optics Question

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SUMMARY

The discussion focuses on calculating the range of lens powers achievable by the human eye's lens and cornea combination. The eye's structure is approximated with a fixed corneal focal length and a variable lens focal length, with the lens positioned 17mm from the retina. Using the lens formula \(1/u + 1/v = 1/f\) and the power equation \(Power = 1/f\), participants estimate the lens power for object distances from 25cm to infinity, concluding that the total power can be derived by combining the individual powers of the cornea and lens.

PREREQUISITES
  • Understanding of basic optics principles, specifically lens formulas.
  • Familiarity with the concept of lens power and focal length.
  • Knowledge of the anatomy of the human eye, particularly the cornea and lens.
  • Ability to perform calculations involving object distance and image distance.
NEXT STEPS
  • Study the lens formula in detail, focusing on its application in optical systems.
  • Research the anatomy of the human eye, emphasizing the roles of the cornea and lens.
  • Explore the concept of accommodation in the eye and its impact on lens power.
  • Learn about optical power calculations in other optical devices, such as cameras and microscopes.
USEFUL FOR

Students studying optics, ophthalmologists, and anyone interested in the mechanics of vision and lens power calculations.

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Homework Statement



The human eyeball is approximately spherical with a diameter of around 25mm. At the back of the eye is the retina, while at the front is a compound lens comprising the cornea (of fixed focal length) and the lens itself (with variable focal length), which can be approximated as a thin lens at a distance of 17mm from the retina. The eye is capable of focusing on objects at distances varying from the near point (about 25cm) to infinity. Estimate the range of lens powers which can be achieved by the lens and the cornea in combination.

Homework Equations



Power = 1/f
1/u + 1/v = 1/f


The Attempt at a Solution



I was wondering if we could get the expression for 1/f for each one of the cornea and the lens, and them add them and take the reciprocal to find the total power, though I am not sure whether it applies to this case?

As far as the range is concerned, I presume it basically entails taking the object distance to be at infinity and at the near point (25cm)

Any help would be great.
 
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With the object at infinity you get f (and the power of the lens combination) directly from the retinal distance.
The other extreme is with the object at 25cm. The focal length (and power) is found in this case using the lens formula you have quoted.
This gives the range of powers.
 

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