Question

In a single slit diffraction experiment. fir t minimum for red light (589 nm) coincides with first maximum of some other wavelength `lambda'`. The value of `lambda'` is ______.

Options

• 4400 Å

• 6642 Å

• 3926 Å

• 3500 Å

Answer 1

In a single slit diffraction experiment. fir t minimum for red light (589 nm) coincides with first maximum of some other wavelength `lambda'`. The value of `lambda'` is 3926 Å.

Explanation:

n a single slit diffraction experiment, position of minima is given by, d sin ` theta = "n" lambda`

So, for first minima of red, sin` theta =1 xx (lambda_"R"/"d")`

and as first maxima is midway between first and second minima, for wavelength `lambda'` its position will be

d sin  ` theta' = lambda' + (2lambda')/2 =>` sin `theta = (3lambda')/(2"d")`

According to given condition sin 0 = sin ` theta` - sin `theta'`

∴ `lambda' = 2/3 lambda_"R"`

∴ `lambda' = 2/3 xx 589 = 392.6` nm = 3926 Å