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?

Options

A. 16
B. 20
C. 24
D. 32

Answer

a

Explanation

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.