In the YDSE apparatus shown in figure, `dltltD` and `d = 6lambda`. Find

(a) total number of maximas and minimas on the screen .
(b) two y-coordinates corresponding to third order maxima.

Explanation

(a) In the given set up, `dltltD`
Therefore, we can apply
` Deltax =d sin theta `
`(Deltax)_min = 0` at `theta = 0^@` and
`(Deltax)_max = 6lambda` at` theta = 90^@`
Therefore, total number of maximas are eleven corresponding to,
`Deltax = 0, +-lambda, +-2lambda, +-3lambda, +-4lambda and +-5lambda`
(b) Third order minima lies at
`Deltax = +-3lambda`
`:. d sin theta = +-3lambda or 6 lambda sin theta = +-3 lambda `
or sin theta = +- 1/2` or `theta = +-(30^@)`
Now, `y/D = tan theta` and `y= D tan theta`
`:. y = +-D tan30^(@)` or `y=+- D/sqrt3`.