The Fire in the Eye You have certainly seen the reflected light from the eyes of...

The Fire in the Eye

You have certainly seen the reflected light from the eyes of a cat or a dog at night. This “eye shine” is the reflection of light from a layer at the back of the eye called the tapetum lucidum (Latin for “bright carpet”). The tapetum is a common structure in the eyes of animals that must see in low light. Light that passes through the retina is reflected by the tapetum back through the cells of the retina, giving them a second chance to detect the light.

Sharks and related fish have a very well-developed tapetum. Figure V.2 a shows a camera flash reflected from a shark’s eye back toward the camera. This reflected light is much brighter than the diffuse reflection from the body of the shark. How is this bright reflection created?

Figure V.2 b shows a typical tapetum structure for a fish. (The tapetum in land animals such as cats, dogs, and deer uses similar principles but has a different structure.) The reflection comes from the interfaces between two layers of nearly transparent cells (whose index of refraction is essentially that of water) and a stack of guanine crystals sandwiched between. Light is reflected from the interface at both sides of the stack of crystals. For certain wavelengths, constructive interference leads to an especially strong reflection.

Bright light from a distant source is focused by the lens of a shark’s eye to a point on the retina, as shown in Figure V.2 c. The tapetum reflects these rays back through the lens, where refraction bends them into parallel rays traveling back toward the source of the light. Because the reflected light from the tapetum is directional, it is much brighter than the diffuse reflection from the shark’s body. But the bright reflection is seen by an observer—or a camera—only at or near the source of the flash that produced the reflection.

What is the (approximate) smallest thickness of the crystal layer that would lead to constructive interference between the front reflection and the rear reflection for light of wavelength 600 nm?

A. 80 nm

B. 160 nm

C. 240 nm

D. 320 nm