An experiment is set-up with a laser, a single slit , and a screen, similar to w

Question

An experiment is set-up with a laser, a single slit, and a screen, similar to what is shown on page 7-2 of your lab manual. The experimenter measures and sketches the intensity pattern shown below.

The scale along the bottom of the figure is in centimeters. What is the distance 2x1 between the first minima in the intensity pattern? (Units required, and you must be within 1 mm to be correct.)

2x1 =

The slit-to-screen distance is D = 1.600 m, and the laser wavelength is 633 nm, use the formula for single-slit diffraction minima to find the slit width a. (Units required.)

a =

If the screen to slit distance were changed to 0.800 m, what would the distance between the first minima 2x1 become? (Units required.)

When D = 0.800 m then 2x1 =

Explanation / Answer

Hi,

1. The distance x1 (the distance from the central maximum to the first minimum), according to the figure is:

x1 = 1.6 cm

Which means that the distance between the first minima is:

2x1 = 3.2 cm

Note: this depends on the accuracy of the observer.

2. The formula that we must use is the following:

a sin() = n ; where is the wavelength of the incident light, a is the width of the slit, n is an integer (which in this case, as we are finding dealing with the first minimun, its value is 1) and is an angle that fulfills the following:

tan() = xn / D

As for the first minimum we have the following:

tan() = x1/D = 1.6*10-2 m/1.6 m ::::::::::::: tan() = 0.01 ::::::::::: = 0.57°

a = / sin() = 633*10-9 m / sin(0.57°) = 6.36*10-5 m = 0.064 mm

3. If now the distance is changed, then the new value of the distance between the first minima would be:

sin() = / a = 633*10-9 m /  6.36*10-5 m = 0.01 ::::::::::: sin() = 0.01 :::::::::: = 0.57° (the angle doesn't change)

tan() = x1/D ::::::::: x1 = D*tan() = (0.800 m)tan(0.57°) = 7.96*10-3 m = 7.96 mm

2x1 = 1.592 cm , which is approximately, 1.6 cm (just a half of the previous value)

Note: the distance between the minama is proportional to the distance between the slit and the screen.

I hope it helps.

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