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Chapter 1: Q46P (page 1)

Visible light is incident perpendicularly on a grating with 315 rulings/mm. What is the longest wavelength that can be seen in the fifth-order diffraction?

Short Answer

Expert verified

635nm

Step by step solution

01

Identification of the given data

The given data is listed below as:

  • The Grating is 315 rulings/mm .
02

The condition of the diffraction grating

The condition of the diffraction grating is:

dsinθ=mλdsinθ=mλ

Here, d is the distance between adjacent rulings and λ is the wavelength of light.

03

 Step 3: To find the longest wavelength that can be seen in the fifth-order diffraction

For the mth order diffraction maximum, the angular location is given by,

dsinθ=mλ

Now, to find the longest wavelength for the fifth-order diffraction

Let’s assume, sinθ|m=5=5λd<1.

Or, λ<d5

λ=1nm/3155λ=635mm

Thus,the longest wavelength that can be seen in the fifth order diffraction is 635 nm.

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