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Two point sources separated by 2.0 m are...

Two point sources separated by 2.0 m are radiating in phase with `lambda = 0.50 m`. A detector moves in a circular path around the two sources in a plane containing them. How many maxima are detected?

A

16

B

20

C

24

D

32

Text Solution

Verified by Experts

The correct Answer is:
a
Condition for maxima is
`d sin theta = n lambda`
`sin theta = (n lambda)/(d) = n ((0.50)/(2.0)) = 0.25 n`
A `sin theta` lies between -1 and 1, so we wish to find all values of n for which
`|0.25n|le 1`
These value are -4, -3, -2, -1, 0, +1, +2, +3, +4. For each of these, there are two different values of theta except for -4 and +4 A single value of `theta,-90^(@)` and `+90^(@)`, is associated with `n = -4` and `n = +4`, respectively. Thus, there are 16 different angles in all and therefore 16 maxima.
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