Under bright light, the pupil of the eye (the circular opening through which lig

Question

Under bright light, the pupil of the eye (the circular opening through which light enters) is typically 2.0 mm in diameter. The diameter of the eye is about 25 mm. Suppose you are viewing something with light of wavelength 460 nm. Ignore the effect of the lens and the vitreous humor in the eye.

1) At what angle will the first diffraction dark ring occur on either side of the central bright spot on the retina at the back of the eye? Express your answer in radians. (Express your answer to two significant figures.)

2) At what angle will the first diffraction dark ring occur on either side of the central bright spot on the retina at the back of the eye? Express your answer in degrees. (Express your answer to two significant figures.)

3) Approximately how far from the central bright spot would the first dark ring occur? (Express your answer to two significant figures.)

4) At what angle will the second diffraction dark ring occur on either side of the central bright spot on the retina at the back of the eye? Express your answer in radians. (Express your answer to two significant figures.)

5) At what angle will the second diffraction dark ring occur on either side of the central bright spot on the retina at the back of the eye? Express your answer in degrees. (Express your answer to two significant figures.)

6) Approximately how far from the central bright spot would the second dark ring occur? (Express your answer to two significant figures.)

7) At what angle will the third diffraction dark ring occur on either side of the central bright spot on the retina at the back of the eye? Express your answer in radians. (Express your answer to two significant figures.)

8) At what angle will the third diffraction dark ring occur on either side of the central bright spot on the retina at the back of the eye? Express your answer in degrees. (Express your answer to two significant figures.)

9) Approximately how far from the central bright spot would the third dark ring occur? (Express your answer to two significant figures.)

Explanation / Answer

Here,

wavelength = 460 nm

slit width = diameter , d = 2 mm

screen distance , D = 25 mm

1) for angle of first diffraction

d * sin(theta) = 1 * wavelength

2 * 10^-3 * sin(theta) = 460 * 10^-9

solving for theta = 2.3 *10^-4 radian

2)

for the angle in degree

theta = 2.3 *10^-4 radian * 180 degree/(3.141 radian)

theta = 0.0132 degree

3)

NOw, for the distance

distance = D * sin(theta)

distance = 25 * sin(2.3 *10^-4 radian)

distance = 5.75 *10^-6 m

the distance of first order minima is 5.75 *10^-6 m

4)

for the second dark ring

d * sin(theta) = 2 * wavelength

2 * 10^-3 * sin(theta) =2 * 460 * 10^-9

solving for theta = 4.6 *10^-4 radian

5)

for angle in degree

theta = 4.6 *10^-4 radian* 180 degree/(3.141 radian)

theta = 0.0264 degree

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please post rest in a seperate post

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