detineerlf

2022-07-20

Can the spectral properties of a light source be predicted from the first-order diffraction patterns?

### Answer & Explanation

Wayne Everett

The objective is to find that can the spectral properties of a light source be predicted from the first order diffraction patterns
Yes,
The principal maxima in a grating satisfy the following condition,
$\left(e+d\right)\mathrm{sin}\theta =n\lambda$
Where,
(e+d) is the grating element
n is the order of the maxima
$\lambda$ is the wavelength of the incident light
The maximum angle of diffraction is ${90}^{\circ }$ hence the maximum possible order is given as follows,
${n}_{\text{max}}=\frac{\left(e+d\right)\mathrm{sin}{90}^{\circ }}{\lambda }=\frac{\left(e+d\right)}{\lambda }$
Here on considering a grating which is having element which is less than twice the wavelength of the incident light then $\left(e+d\right)<2\lambda$
Therefore,
${n}_{\text{max}}<\frac{2\lambda }{\lambda }<2$
That is only the first order is possible

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