Chapter 25, Problem 52RPP

BIO Amazing honeybees The survival of a bee colony depends on the ability of bee scouts to locate food and to convey that information to the hive. After finding a promising food source, a honeybee scout returns to the hive and uses a waggle dance to tell its worker sisters the direction and distance to the food.

Recall that light coming directly from the Sun is unpolarized. Bees use the direction of the Sun as a reference for their travel. In the hive, the scout bee's waggle dance is in the shape of a flat figure eight (Figure 25.28). The upward direction in the vertical hive represents the direction toward the Sun. The middle line of the scout’s figure eight points in the direction of the food relative to the direction of the Sun. I hus a $50°$ middle waggle dance to the right of the vertical in the hive would indicate a food source outside that is $50°$ to the right of the direction toward the Sun The distance to the food depends on the length of time the scout takes while wiggling her tail and wings through this middle of the figure eight. The other bees know the direction to the food even if the Sun is behind a cloud—they can detect the degree of polarization in other open parts of the sky and deduce the angle to the Sun from that position, and they learned from the scout the angle from the Sun's direction to the food.

If the direction of the middle line of the scout's waggle dance figure eight points $53°$ to the left side of the upward direction in the hive, in what direction to the left should bees leaving the nest for the food source head relative to light coming from the Sun?

a. Where the light is $36\%$ linearly polarized to the left of the Sun’s direction

b. Where the light is $60\%$ linearly polarized to the left of the Sun’s direction

c. Where the light is $64\%$ linearly polarized to the left of the Sun’s direction

d. Where the light is $80\%$ linearly polarized to the left of the Sun’s direction

e. Where the light is $100\%$ linearly polarized to the left of the Sun’s direction