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. (a) `16`
B. (b) `20`
C. (c) `24`
D. (d) `32`

Answer

A

Explanation

Condition for maxima is
`dsin theta=nlambda`
`sin theta=(nlambda)/(d)=n((0.50)/(2.0))=0.25n`
As sin q lies between -1 and 1, so we wish to find all values of n for which
`|0.25n|le1`
These values are -4, -3, -2, -1, 0, +1, +2, +3, +4. For each of these there are 2 different values of q except for -4 and +4. A single value of q, `-90^@` and `+90^@`, is associated with `n=-4` and `n=+4` respectively. Thus there are 16 different angels in all and therefore 16 maxima.