Dispersion by diffraction grating

In summary, the conversation involves a question about the width of the first-order spectrum on a screen 2.15 m away when white light with wavelengths from 396 nm to 756 nm falls on a grating with 7300 lines/cm. The equation used is y=m*L*wavelength/(d) and the attempt at a solution involves finding the difference between y1 and y2, which gives a value of 56.486 cm. However, there is some confusion about the equation and its units, and the correct answer is found to be 56.502 cm.
  • #1
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Homework Statement



White light containing wavelengths from 396 nm to 756 nm falls on a grating with 7300 lines/cm. How wide is the first-order spectrum on a screen 2.15 m away?

Homework Equations


y=m*L*wavelenth/(d)


The Attempt at a Solution


using the equation I have found y1 to be 62.149 and y2 118.635. I took the difference of the two which gave me 56.486 cm, but that is wrong for some reason. Please help.
 
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  • #2
Are you sure of that that's the equation for diffraction? Checking the units, it's quite inconsistent... Check the equation again...
 
  • #3
That's the equation I'm used to. If we assume that the angle is small then sintheta=y/L
dsintheta=m*wavelength
d(y/L)=m*wavelength
m*wavelength*L/(d)=y ? I don't know what's wrong with the equation. For the units I converted everything to cm because 1/7300=d in cm.
 
  • #4
Please help, I only have a couple of hours left.
 
  • #5
I got 56.502 cm, using the equation. we seem to get the same answer.
 
Last edited:

FAQ: Dispersion by diffraction grating

1. What is dispersion by diffraction grating?

Dispersion by diffraction grating is the phenomenon where a beam of light passing through a grating is separated into its component colors, or wavelengths. This is due to the diffraction of light as it passes through the narrow slits on the grating.

2. How does a diffraction grating work?

A diffraction grating is made up of a series of closely spaced parallel lines, or slits, that act as obstacles to the passing light. When the light encounters these slits, it is diffracted and spreads out into a spectrum of colors.

3. What is the relationship between the spacing of the grating and the resulting spectrum?

The spacing of the grating, also known as the grating constant, determines the angle at which the different colors are dispersed. A smaller spacing will result in a wider dispersion angle, while a larger spacing will result in a narrower dispersion angle.

4. What are some real-world applications of dispersion by diffraction grating?

Diffraction gratings are commonly used in spectroscopy, which is the study of the interaction between light and matter. They are also used in optical instruments such as spectrometers and monochromators to analyze and separate different wavelengths of light.

5. How is dispersion by diffraction grating different from other forms of dispersion?

Dispersion by diffraction grating is based on the diffraction of light, while other forms of dispersion, such as refraction and reflection, are based on the bending of light. Diffraction grating dispersion is also more precise and can separate light into a larger number of distinct wavelengths compared to other methods.

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