A single slit is illuminated with light of wavelength 632.8 nm. The width of the

Question

A single slit is illuminated with light of wavelength 632.8 nm. The width of the slit is 83.4micrometers and the light is reflecting off a screen 1.70m behind the slit.

1. At what distance is the first maxima located from the center of the pattern (in m)?

2. At what distance is the second maxima located from the center of the pattern (in m)?

3. At what distance is the third maxima located from the center of the pattern (in m)?

4. At what distance is the first minima located from the center of the pattern (in m)?

5. At what distance is the second minima located from the center of the pattern (in m)?

6. At what distance is the third minima located from the center of the pattern (in m)?

Thank you for your help! I'm a bit confused as to how to go about tackleing this problem.

Explanation / Answer

wavelength = 632.8 nm = 632.8 x 10-9 m

width = d = 83.4 um = 83.4 x 10-6 m

distance of screen = D = 1.70 m

x = position of maxima from center

1.

position of maxima is given as

x = (2m + 1) (lamda)D/d

for first maxima , m = 1

X = (2(1) + 1) (632.8 x 10-9) (1.70) / (83.4 x 10-6)

X = 0.0387 m

2.

position of maxima is given as

x = (2m + 1) (lamda)D/d

for second maxima , m = 2

X = (2(2) + 1) (632.8 x 10-9) (1.70) / (83.4 x 10-6)

X = 0.0645 m

3.

for third maxima , m = 3

X = (2(3) + 1) (632.8 x 10-9) (1.70) / (83.4 x 10-6)

X = 0.0903 m

4.

position of maxima is given as

x = (m) (lamda)D/d

for first minima , m = 1

X = (1) (632.8 x 10-9) (1.70) / (83.4 x 10-6)

X = 0.0129 m

5.

for second minima , m = 2

X = (2) (632.8 x 10-9) (1.70) / (83.4 x 10-6)

X = 0.0258 m

6.

for third minima , m = 3

X = (3) (632.8 x 10-9) (1.70) / (83.4 x 10-6)

X = 0.0387 m

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