Question

A. The human eye 1. Whenever a normal eye forms an image, the image distance will always equal the distance from the cornea and eye lens to the retina (~25 mm), regardless of how far away the object is located. Explain why the image distance cannot change. 2. If the image distance must change, then what intrinsic property of the eye lens must change in order for the eye to focus on objects at different distances? Hint: read the Introduction. We will first model the cornea plus the eye lens as a single thin lens, which we will refer to as “the eye.” 3. Assuming normal vision, when the eye is focused on a distant object (object distance = ?), what its approximate focal length? 4. What is the approximate focal length of the eye when it is focused on an object at the near point, the closest distance at which you can comfortably focus (about 25 cm from the eye for normal vision)? In ophthalmology a lens is described by its refractive power, which is the inverse of its focal length. The unit of refractive power is the diopter (symbol D), which is equal to an inverse meter (m-1). 5. What is the refractive power of the normal eye when forming an image of a distant object? 6. What is the refractive power of the normal eye when forming an image of an object at the near point? When the eye adjusts its focus the refractive power of the cornea remains the same while the shape of the eye lens (and thus its refractive power) changes. To see what changes in refractive power are required, we now consider how the refractive power of the eye depends on the individual refractive powers of the cornea and the eye lens. The cornea and the eye lens are separated by a small distance, but for simplicity we will model the cornea and eye lens as two separate thin lenses that are physically touching one another (i.e., the spacing between the two lenses is zero). 7. Ignoring the eye lens for the moment, if light comes from a distant object, at what location from the cornea (of focal length f c ) is the image formed? Express your answer in terms of f c . 8. The image produced by the cornea is the object for the eye lens. What is object distance for the eye lens? Express your answer in terms of f c . Hint: think about the sign of the object distance. 9. If the eye lens has a focal length f e , then how far from the eye lens will the image it creates be located? Express your answer in terms of f c and f e . The image created by the eye lens should fall on the retina if the eye is properly focused. 10. If we model the cornea and eye lens as a single thin lens (of focal length f ce), then at what distance from this lens will the image of a distant object be formed? Express your answer in terms of f ce. The image created by the cornea and eye lens together should also fall on the retina if the eye is properly focused. 11. Is the image distance you found in question A9 greater than, less than, or equal to the image distance you found in question A10? Explain. 12. Use your answers to questions A10 and A11 to write down an equation relating f ce, f c , and f e . 13. Use your answer to question A12 to write down an equation relating the refractive power of the cornea and eye lens together in terms of the refractive powers of the cornea and eye lens individually. ü Check your answer with an instructor before proceeding. 14. Why might it be convenient to think in terms of refractive power rather than focal length? The refractive power of the cornea is about 38 diopters. 15. What is the refractive power of the eye lens when the eye is focused on a distant object? Hint: consider your answer to A5. 16. What is the refractive power of the eye lens when the eye is focused on an object at the near point? Hint: consider your answer to A6.

Answer 1

1. Image distance can not change because the distance from the cornea/lens to the retina is fixed and in order to detect an object, its image must be focused on the retina, i.e. image distance must be equal to the distance between the retina and the lens.

2. If image distance must change, then the focal length of the eye lens must change.