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Chapter 36: Q58P (page 1113)

A grating has 600 rulings/mm and is 5.0 mm wide. (a) What is the smallest wavelength interval it can resolve in the third order at ? (b) How many higher orders of maxima can be seen?

Short Answer

Expert verified
  1. The smallest wavelength interval it can resolve in the third order is0.056nm .
  2. No higher orders of the maxima can be seen.

Step by step solution

01

The resolving power

It is known the resolving power of a grating is given byR=Nm=λavg∆λ , where is Nthe number of rulings in the grating and mis the order of the linesλavg, is the average of wavelengths and∆λ is the separation.

02

The wavelength interval

Here, the order ism=3 . So, the wavelength interval can be obtained as follows:

Δλ=λNm=500 nm600×5.0×3=0.056 nm

Thus, the smallest wavelength interval it can resolve in the third order is0.056 nm .

(b)

To find the highest order of the maxima, we havesinθ=mmaxλd<1 . So, the value of highest order of the maxima is:

mmax<dλ<1600500×10-6mm<3.3

Since, the order can be a whole number, so, the highest order is 3.

Thus, no higher orders of the maxima can be seen.

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