Answer:
[tex]\lambda= 506.25 nm[/tex]
Explanation:
Diffraction is observed when a wave is distorted by an obstacle whose dimensions are comparable to the wavelength. The simplest case corresponds to the Fraunhofer diffraction, in which the obstacle is a long, narrow slit, so we can ignore the effects of extremes.
This is a simple case, in which we can use the Fraunhofer single slit diffraction equation:
[tex]y=\frac{m \lambda D}{a}[/tex]
Where:
[tex]y=Displacement\hspace{3}from\hspace{3} the\hspace{3} centerline \hspace{3}for \hspace{3}minimum\hspace{3} intensity =1.35mm\\\lambda=Light\hspace{3} wavelength \\D=Distance\hspace{3}between\hspace{3}the\hspace{3}screen\hspace{3}and\hspace{3}the\hspace{3}slit=2m\\a=width\hspace{3}of\hspace{3}the\hspace{3}slit=0.750mm\\m=Order\hspace{3}number=1[/tex]
Solving for λ:
[tex]\lambda=\frac{y*a}{mD}[/tex]
Replacing the data provided by the problem:
[tex]\lambda=\frac{(1.35\times 10^{-3})*(0.750\times 10^{-3})}{1*2} =5.0625\times 10^{-7}m =506.25nm[/tex]
The wavelength of the light will be "506.25 nm". To understand the calculation, check below.
According to the question,
Displacement, y = 1.35 mm
Distance b/w screen and slit, D = 2 m
Slit's width, a = 0.750 mm
Order number, m = 1
We know the relation,
→ y = [tex]\frac{m \lambda D}{a}[/tex]
Or,
The wavelength, λ = [tex]\frac{y\times a}{mD}[/tex]
By substituting the values,
= [tex]\frac{1.35\times 10^{-3}\times 0.750\times 10^{-3}}{1\times 2}[/tex]
= 5.0625 × 10⁻⁷ m or,
= 506.25 nm
Thus the above answer is correct.
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