Question

Calculate the possible order of spectra with a plane transmission grating having 18,000 lines per inch when light of wavelength 4500 Å is used.

Answer 1

Answer:

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Answer 2

Answer:

Possible Order of spectra is n = 3 .

Explanation:

Step 1:

According to "Bragg's Law",

nλ=dsinθ

where, n = order of spectra (order of reflection)

λ=  wavelength

d = Interplanar spacing or distance between two planes.

θ= Angle between the wave vector of the incident plane wave.

Step2:

In the question given :

N = No. of grated lines per unit wavelength = 18000 lines/inch

So, lines per meter will be = $\frac{18000}{ 0.0254}$ = 7.09×10⁵  lines/m

Wavelength of light, λ= 45000 A=$45000*10^{10} m$

SO, highest order will occur when sinθ=1

Step3:

Then, the Expression becomes,

⇒n=d/λ

⇒Since d=1/N

⇒n=1/Nλ

⇒$n=\frac{1}{(7.09*10^{5})(4500*10^{-10} ) }$

⇒n=3

Hence,the possible order of spectra can be 3.