The human eye can be approximated by a two-lens optical system. Light enters the eye and first travels through the cornea and aqueous humor. The cornea and aqueous humor are sometimes called the aqueous lens. The aqueous lens of a sample eye has a focal length of 4.16666 cm. The iris blocks some of the light that travels through the aqueous lens. Next, light travels through the center of the crystalline lens and vitreous humor to the retina. The crystalline lens and the vitreous humor can be approximated by one lens, called the crystalline lens, with a focal length that can change. For healthy eyes, the crystalline lens is set 0.50000 cm behind the aqueous lens and can vary in focal length from 9.0000 cm to 16.5000 cm. The retina acts as an image screen upon which real images are focused for processing by the brain. The retina is 3.0000 cm behind the crystalline lens. b) When the muscles connected to the crystalline lens contract fully, its focal length is 16.5000 cm. With this focal length, how far away must an object be to form sharply focused images on the retina? (Note: this distance is called the far point of vision.)

c) When the muscles connected to the crystalline lens relax, the focal length is 9.0000 cm. With this focal length, how close must an object be to form sharply focused images on the retina? (Note: this distance is called the near point of vision.)

d) As people age, the crystalline lens hardens (a condition called presbyopia or “old-age” eyes) and can only vary in focal length from 12 to 15.60 cm. Calculate range of vision (the new near point and far point) for this older eye.
e) Based on part d) why might an older person hold the newspaper at arm’s length to read it?