First slide

Young's double slit Experiment

Question

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

Moderate

A

16
B

20
C

24
D

32

Solution

Condition for maxima is
$dsinθ = nλ$
$sinθ = \frac{nλ}{d} = n (\frac{0 .50}{2 .0}) = 0 .25 n$
As $\sin θ$ lies between $- 1 and 1,$ so we wish to find all values of n for which
$| 0.25 n | \leq 1$
These values are $- 4, - 3, - 2, - 1, 0, + 1, + 2, + 3, + 4$ . For each of these there arc 2 different values of q except for $- 4 and + 4$ . A single value of $θ$ , $- 90^{\circ} and + 90^{\circ},$ 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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