Figure (17-E5) shows three equidistant slits being illuminated by a monochromatic parallel beam of light. Let BP₀ - AP₀ = λ/3 and D >> λ. (a) Show that in this case . (b) Show that the intensity at P₀ is three times the intensity due to any of the three slits individually.

Question

Figure (17-E5) shows three equidistant slits being illuminated by a monochromatic parallel beam of light. Let BP₀ - AP₀ = λ/3 and D >> λ. (a) Show that in this case

. (b) Show that the intensity at P₀ is three times the intensity due to any of the three slits individually.

Philoid · Accepted Answer

(a)In the problem, it’s given BP₀ - AP₀ = λ/3

From the figure and using Pythagoras theorem,

Ignoring as its small as compared to others.

(b) The distance of from the line in the middle of B and C is

The path difference between waves coming from B and C is

This means that they are in phase.

But the wave coming from A has a phase difference,

Let the amplitude from each slit be a. Therefore, contribution from B and C is 2a.

And the resultant intensity taking in consideration the phase difference,

Therefore, the ratio of total intensity by individual intensity is

So the intensity at P₀ is three times the individual intensity.

Figure (17-E5) shows three equidistant slits being illuminated by a monochromatic parallel beam of light. Let BP0 - AP0 = λ/3 and D >> λ. (a) Show that in this case . (b) Show that the intensity at P0 is three times the intensity due to any of the three slits individually.

Figure (17-E5) shows three equidistant slits being illuminated by a monochromatic parallel beam of light. Let BP₀ - AP₀ = λ/3 and D >> λ. (a) Show that in this case . (b) Show that the intensity at P₀ is three times the intensity due to any of the three slits individually.