Figure 4 - Diffraction of a single slit. Comparing Figure 4 with Figure 2, one c

Question

Figure 4 - Diffraction of a single slit.
Comparing Figure 4 with Figure 2, one can draw the conclusion that the double slit fringe pattern is actually composed of two effects, the interference between the light sources from the two slits and the diffraction pattern from each slit. Since the slits are very close to each other, the diffraction pattern from each slit superimposes each other.

Figure 5 - Diffraction pattern from a single slit.

The next two parts will make use of Figure 5.

What is the distance from the central maximum (indicated by the black arrow) to the first minimum (middle of the white area)? (This distance is y in Figure 4.)

Use the equation for a single slit, calculate the width, D of the slit. The distance from the slit to the screen, L is kept at 1.56 m. The angle can be calculated by using Figure 4.

Explanation / Answer

given,

distance from the slit to the screen, L = 1.56 m

y = 1 cm or 1 * 10^-2 m (from the figure)

the distance from the central maximum to the first minimum = 1 cm

D * sin(theta) = n * wavelength

sin(theta) = y / (y^2 + L^2)^(1/2)

sin(theta) = (1 * 10^-2) / ((1 * 10^-2)^2 + 1.56^2)^(1/2)

theta = 0.3673 degree

D * sin(0.3673) = wavelength

D = wavelength / sin(0.3673)

the width, D of the slit = wavelength / sin(0.3673)

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