Suppose you had the same laser and diffraction grating from the previous question but now you had a flat detection screen. You want to use this set up to measure the displacement due to small vibrations of the detection screen. (The vibrations cause the screen to move closer and farther from the grating.) A. Describe how you would do measurements for this experiment to determine the displacement of the detection screen.

measuring the zero intensity point, we can deduce the movement of the screen.

The distance from the center of the pattern to the first zero is proportional to the distance to the screen,

Explanation:

The expression for the diffraction phenomenon is

           a sin θ = m λ

for the case of destructive interference. In general the detection screen is quite far from the grid, let's use trigonometry to find the angles

           tan θ = y / L

in these experiments the angles are small

          tan θ = sin θ / cos θ = sin θ

          sunt θ = y / L

we substitute

          a = m  λ

           y = m L λ / a

therefore, by carefully measuring the zero intensity point, we can deduce the movement of the screen.

The distance from the center of the pattern to the first zero is proportional to the distance to the screen, so you can know where the displacement occurs, it should be clarified that these displacements are very small so the measurement system must be capable To measure quantities on the order of hundredths of a millimeter, a micrometer screw could be used.

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