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In Fig. 35-37, two radio frequency point sources S1and S2, separated by distance d=2.0m, are radiating in phase with λ=0.50m. A detector moves in a large circular path around the two sources in a plane containing them. How many maxima does it detect?

Short Answer

Expert verified

The total number of the maxima is 16.

Step by step solution

01

Write the given data from the question

The distance between the slits, d=2m.

The wavelength, λ=0.50m.

02

Determine the formulas to calculate the number of the maxima detect by the detector

The condition for the maxima in Young’s experiment is given as follows.

dsinθ=mλ …… (1)

Here,d is the distance between the slits, λis the wavelength, mis the order, andθis the angular separation.

03

Calculate the number of the maxima detect by the detector

Calculate the number of the maxima.

Substitute 0.50mfor λand 2m for d into equation (1).

2sinθ=m×0.50sinθ=12×m×0.50sinθ=14×m

Now,

sinθ⩽1m4⩽1.

The value of m can be negative as well as positive. Therefore, m will have -4,-3,-2,-1,0,+1,+2,+3,+4.

For each of the value there is two values of the θ.

Therefore, one value for -900Cand other for +900C.

Hence, the total number of the maxima is 16.

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