To solve this problem we will apply the concepts given by the principles of superposition, specifically those described by Bragg's law in constructive interference.
Mathematically this relationship is given as
[tex]dsin\theta = n\lambda[/tex]
Where,
d = Distance between slits
[tex]\lambda[/tex] = Wavelength
n = Any integer which represent the number of repetition of the spectrum
[tex]\theta = sin^{-1} (\frac{n\lambda}{d})[/tex]
Calculating the value for n, we have
n = 1
[tex]\theta_1 = sin^{-1} (\frac{\lambda}{d})\\\theta_1 = sin^{-1} (\frac{632.8*10^{-9}}{1.6*10^{-6}})\\\theta_1 = 23.3\°[/tex]
n=2
[tex]\theta_2 = sin^{-1} (\frac{2\lambda}{d})\\\theta_2 = sin^{-1} (2\frac{632.8*10^{-9}}{1.6*10^{-6}})\\\theta_2 = 52.28\°[/tex]
n =3
[tex]\theta_2 = sin^{-1} (\frac{2\lambda}{d})\\\theta_2 = sin^{-1} (3\frac{632.8*10^{-9}}{1.6*10^{-6}})\\\theta_2 = \text{not possible}[/tex]
Therefore the intensity of light be maximum for angles 23.3° and 52.28°
