Light of wavelength 625.0 nm is incident normally on a diffraction grating. Two

Question

Light of wavelength 625.0 nm is incident normally on a diffraction grating. Two adjacent maxima occur at angles given by sin ? = 0.260 and sin ? = 0.360. The fourth-order maxima are missing.

1)What is the separation between adjacent slits?

2)What is the smallest slit width this grating can have?

3)For that slit width, what the largest value of the order number m of the maxima produced by the grating

4)What is the second largest largest value of the order number m of the maxima produced by the grating?

5)What is the third largest value of the order number m of the maxima produced by the grating?

Explanation / Answer

so m lambda = d sin theta

and (m +1) lambda = d sin theta

so subtract equations

lambda = d (sin theta - sin theta)

d = 625.0E-9/(0.36-0.26)= 6.25E-6 m or 6.25 um

2)

since m=4 is missing this has to correspond to first diffraction min

lambda = a sin theta

but 4 lambda = d sin theta

divide equation

4 lambda/lambda = d sin theta/a

a = d/4 = 6.25E-6/4 = 1.56E-6 m or 1.56 um

3) so max based on slit splacing is when theta = 90

m lambda = d sin (90)

m = d/lambda = 6.25E-6/625.0E-9= 10

there will diffraction min at 4 and 8

so 10 is largest
4) 9 is second

5) 7 is third

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