To solve this problem it is necessary to apply the related concepts to the principle of overlap, specifically to single slit diffraction experiment concept.
Mathematically this can be expressed as:
[tex]dsin\theta = m\lambda[/tex]
Where,
d = Width of the slit
[tex]\lambda =[/tex]Wavelength
[tex]\theta =[/tex] Angle relative to the original direction of the light
m = Any integer which represent the order of the equation (number of repetition of the spectrum)
To solve the problem we need to rearrange the equation and find the wavelength
[tex]\lambda = \frac{dsin\theta}{m}[/tex]
Our values are given as,
[tex]d = 1.46\mu m = 1.46*10^{-6}m[/tex]
[tex]\theta = 21\°[/tex]
[tex]m = 1[/tex]
Replacing in our equation we have,
[tex]\lambda = \frac{dsin\theta}{m}[/tex]
[tex]\lambda = \frac{(1.46*10^{-6})sin(21)}{1}[/tex]
[tex]\lambda = 5.232*10^{-7}m[/tex]
[tex]\lambda = 523.2nm[/tex]
Therefore the wavelength is 523.2nm
