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Coherent monochromatic light of wavelength λ in air is incident on two narrow slits, the centers of which are 2.0 mm apart, as shown above. The interference pattern observed on a screen 5.0 m away is represented in the figure by the graph of light intensity I as a function of position x on the screen.

a. What property of light does this interference experiment demonstrate?

b. At point P in the diagram, there is a minimum in the interference pattern. Determine the path difference between the light arriving at this point from the two slits.

c. Determine the wavelength, λ, of the light.

d. Briefly and qualitatively describe how the interference pattern would change under each of the following separate modifications and explain your reasoning.

i. The experiment is performed in water, which has an index of refraction greater than 1.

ii. One of the slits is covered.

iii. The slits are moved farther apart.

1 Answer

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(a) The fact that light interferes means it’s a wave (this will be discussed more in the modern physics topic)

(b) Looking at the intensity pattern, P is the second point of zero intensity which means it’s the 2nd dark spot (m = 1.5).

Using Path Diff = mλ … m λ = dx / L … path diff = (2x10–3) (1.8x10–3) / 5 … path diff = 7.2x10–7m

(c) Path Diff = mλ … 7.2x10–7 = 1.5 λ … λ = 4.8x10–7 m

(d) (i) Based on n1 λ1 = n2 λ2 … nair λair = nwater λwater. The λwater is less in comparison to the air. So the λ has been decreased. In the equation m λ = d x / L, for decreased λ there will be decreased x, which means the location of spots is smaller, compressing the pattern.

(ii) Covering a slit makes this a single slit pattern. In the single slit, m = 1 becomes the first dark region (the end of the central bright spot) instead of m = 0.5 being the end of the central bright spot. All of the other integer m’s also become dark spot locations. The effect of this is to make the central max wider and widen the pattern. Additionally, in single slit diffraction, the intensities generally lose intensity more rapidly when moving away from the center.

(iii) Increasing d. Based on mλ = d x / L, this would make x less so would compress the pattern.

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