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Chapter 36: Q47P (page 1112)

A grating has 400 lines/mm. How many orders of the entire visible spectrum (400-700 nm) can it produce in a diffraction experiment, in addition to the order?m=0

Short Answer

Expert verified

There are 3 complete orders on each side of the m=0 order.

Step by step solution

01

Identification of the given data

The given data is listed below as:

  • The visible spectrum is 400 to 700 nm.
  • The order is m=0.
02

The condition of the diffraction grating

The condition of the diffraction grating is:

dsin胃=m位

Here, d is the distance between adjacent rulings, m is an integer, and 位 is the wavelength of light.

03

To find the longest wavelength that can be seen in the fifth-order diffraction

Diffraction lines occur at an angle 胃and is given by,

dsin胃=m位

The ruling separation is:

d=1(400mm-1)=2.5脳10-3mm

Now, take the longest wavelength in the visible spectrum of and find the greatest integer value of m such that the angle 胃<90掳.

Therefore, for m位<d.

So, m=d位

m=2.5脳10-6m700脳10-9mm=3.57

Therefore, consider the value of mas 3.

Thus, there are 3 complete orders on each side of the m=0 order. And the second and third order overlaps.

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