Question

A double slit is illuminated by two wavelengths 450 nm and 600 nm. What is the lowest order at which the maxima of one wavelength coincides with the minima of the other wavelength?

Answer 1

Given:

A double slit is illuminated by two wavelengths 450 nm and 600 nm.

To find:

Lowest order at which maxima of one wavelength coincides with the minima of the other wavelength.

Calculation:

Let n th order maxima of 450nm coincide with the n th order minima of 600nm .

Distance of the maxima from central point on screen :

$\therefore \: d = \dfrac{n \lambda D}{d}$

Distance of the minimum from the central point on the screen :

$\therefore \: d = \dfrac{(2n - 1) (\lambda2) D}{2d}$

Since the maxima and minima coincide :

$\therefore \: \dfrac{n \lambda D}{d} = \dfrac{(2n - 1) (\lambda2) D}{2d}$

$= > \: n \times 450 = \dfrac{(2n - 1) \times 600}{2}$

$= > \: 3n = 4n - 2$

$= > \: n = 2$

Hence , final answer is :

2nd order Maxima will coincide with the second order minima for the given wavelength in YDSE.