Calculating Spectrum Width of White Light on a Diffraction Grating

In summary, the conversation is about calculating the width of the spectrum produced by a diffraction grating when white light is shone onto it. The formula n lamda = d sin theta is mentioned as a way to solve the problem and the use of trigonometry is suggested to find the solution. The concept of entropy is briefly mentioned as well.
  • #1
Velocity
This question really has me stumped..i would appreciate it if anyone could help me out:smile:

White light containing wavelengths of 400nm to 750 nm is shone normally onto a diffraction grating of 3000 lines/cm. Calculate the width of the spectrum that appears as the second antinode on a screen that is 100 cm away.

Is there a specific formula I can use to solve the question? If so then please help.. thanks
 
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  • #2
Yes, use the diffractin grating equation.

n lamda = d sin theta

Rearrange the terms, solve for theta for two cases -- the longest wavelength at the n=2-mode and the shortest wavelength at the n=3-mode. Use this information with the distance between the grating and the screen to solve the problem -- just a little trigonometry.

eNtRopY
 

1. What is a diffraction grating?

A diffraction grating is an optical component that consists of a large number of equally spaced parallel slits or grooves. It is used to separate white light into its component colors through the process of diffraction.

2. How is the spectrum width of white light on a diffraction grating calculated?

The spectrum width of white light on a diffraction grating is calculated using the equation Δλ = d(sinθm), where Δλ is the spectral width, d is the distance between the slits, and θm is the angle of diffraction for the mth order maximum.

3. What factors affect the spectrum width on a diffraction grating?

The spectrum width on a diffraction grating is affected by the distance between the slits, the wavelength of the incident light, and the angle of diffraction.

4. Why is it important to calculate the spectrum width on a diffraction grating?

Calculating the spectrum width on a diffraction grating allows us to accurately determine the wavelengths present in a beam of white light. This is important in various scientific fields, such as spectroscopy and astronomy, where the precise measurement of wavelengths is crucial.

5. Can the spectrum width on a diffraction grating be adjusted?

Yes, the spectrum width on a diffraction grating can be adjusted by changing the distance between the slits or by using a different diffraction grating with a different number of slits per unit length. The angle of diffraction can also be adjusted by changing the position of the diffraction grating or the incident light source.

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