3-1. If red light has a wavelength of 620 nm in a vacuum, what are the wavelength, frequency and speed of this light in the vitreous humour of the eye? (n = 1.34)
 

3-2. What is the speed of light in medium 2 in the figure?

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3-3. The minimum diameter of the pupil of the human eye is about 2 mm and the maximum diameter is about 8 mm. How much more light energy per unit time enters the eye with the pupil fully dilated than when the pupil is at its minimum size?
 

Problems
 

3-4. A thin lens has radii of curvature r_l = + 2.0 cm and r₂ = + 1.0 cm. The glass of which it is made has refractive index 1.5 .
 

(a) What is its power in air?
 

(b) What is its power in water? (n = 1.33)
 

(c) Now suppose that it is placed in a wall on one side of which is air and on the other water. (The surface having radius r₂ in contact with water.) What is the power in this case?
 

(d) In questions (a), (b), and (c) find out where the image of an object placed 10 cm from the lens is formed. What power would the lens in question (b) have to have in order that the image distance be the same as in the question (c)?
 

3-5. Show that a uniform glass sphere of radius R and refractive index n₂, immersed in a medium of index n₁, forms an image of a very distant object at a distance Rn₂/2(n₂ - n₁) from its centre. (See Box 3-5.)
 

3-6. The physical properties of the relaxed eye are given in Table 3-2. With these properties the distance from the cornea to the retina is 25 mm and an object infinitely far away is in focus on the retina. If an object is placed a distance of 1.0 m from the cornea, the eye accommodates by changing the radius of curvature of the posterior surface of the lens. Find the new radius of curvature. Assume that the changes are small enough that the distances between the surfaces remain unchanged.

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