Question

The gnaphosid spider Drassodes cupreus has evolved a pair of lensless eyes for detecting polarized light. Each eye is sensitive to polarized light in perpendicular directions. Near sunset, the spider leaves its nest in search of prey. Light from overhead is linearly polarized and indicates the direction the spider is moving. After the hunt, the spider uses the polarized light to return to its nest. Suppose that the spider orients its head so that one of these two eyes detects light of intensity 700 W/m2and the other eye detects zero light intensity.

Part A: What intensity does the first eye (intensity 700 W/m2 ) detect if the spider now rotates its head 20 ∘ from the previous orientation?

Part B:What intensity does the first eye (zero intensity) detect if the spider now rotates its head 20 ∘ from the previous orientation?

Answer 1

Part A

The intensity is
`I = 618 W/m^2`

Part B

The intensity is
`I_1= 81.884 W/m^2`

Step-by-step explanation:

From the question we are told that

The intensity of the light detected by first eye is
`I = 700 W/m^2`

Now at initial state according the question the light ray is perpendicular to the eye so it means that it is at 90° the eye

Now the first question is to obtain the intensity the first eye (the first in this case is the one focused on the light )would detect when the head is rotated by 20° its previous orientation

This is mathematically evaluated as

`I = I_i cos^2 ( 20^o)`

`I = 700\ cos^2 (20)`

`I = 618 W/m^2`

Now the second question is to obtain the intensity the first eye (the first eye in this case is the one that is not focused on the light )would detect when the head is rotated by 20° its previous orientation

Now in this case the angle between the eye and the light is 90-20 = 70°

So

`I_1 = 700 \ cos^2 (70)`

`I_1= 81.884 W/m^2`