How Many Bright Fringes Appear on the Screen in a Diffraction Experiment?

In summary, the conversation discusses the use of a diffraction grating with 600 lines/mm and light of wavelength 500nm being projected onto a viewing screen 2.0m behind the grating. The question is posed about how many bright fringes can be seen on the screen, and the response involves using the equation d sin theta = m lambda to find the highest order fringe that can appear on the screen. The final solution is determined to be 7 fringes.
  • #1
bigsaucy
38
0
A diffraction grating with 600 lines/mm is illuminated with light of wavelength 500nm. A very wide viewing screen is 2.0m behind the grating.

b.) How many bright fringes can be seen on the screen.

MY ATTEMPT:

i worked out the angular separation between bright fringes to be 0.305 rad (i know this is right because i got the answer to part a right). So then the screen has a total angle of 180 degrees or pi rad. therefore i reasoned that the number of fringes is pi rad/0.305 rad. But since there won't be any bright fringe at 0 rad or pi rad, the final solution must be pi (rad/0.305 rad - 2)

Is this reasoning correct or am I completely off? (Note, the answer is 7 fringes)
 
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  • #2
Hint: What's the highest order fringe visible on the screen?
 
  • #3
Yeah... still not hitting any switches, sorry, lol.
How are we meant to find the number of orders?
 
  • #4
What equation tells you the angle that a bright fringe makes?
 
  • #5
d sin theta = m lambda?
 
  • #6
bigsaucy said:
d sin theta = m lambda?
Exactly. Use that to find the greatest value of m that can appear on screen.
 
  • #7
I don;t get it? How am I meant to solve for something that has two unknown variables? the theta and the m value?
 
  • #8
bigsaucy said:
I don;t get it? How am I meant to solve for something that has two unknown variables? the theta and the m value?
Ah, but theta is not an unknown. What's the largest angle that a fringe could make and still be visible on the screen? (For all practical purposes.)
 

Related to How Many Bright Fringes Appear on the Screen in a Diffraction Experiment?

What is a diffraction grating and how does it work?

A diffraction grating is an optical component that is used to disperse light into its component wavelengths. It consists of a large number of parallel, equally spaced slits or grooves that act as small mirrors to reflect and diffract the light. The spacing between the slits determines the amount of diffraction that occurs, with smaller spacing resulting in greater dispersion of wavelengths.

What are some common problems encountered when using a diffraction grating?

One common problem is light leaking in from the sides of the grating, which can affect the accuracy of the results. Another issue is the presence of unwanted spectral lines, known as higher order diffraction, which can result from imperfections in the grating or its alignment.

How do you calculate the grating spacing or the number of lines per unit length?

The grating spacing, also known as the groove density, can be calculated by dividing the wavelength of the incident light by the angle of diffraction. The number of lines per unit length is simply the inverse of the grating spacing, measured in lines per millimeter or lines per inch.

What are some applications of diffraction gratings?

Diffraction gratings have a wide range of applications in scientific and technological fields. They are commonly used in spectroscopy to analyze the composition of materials based on their unique spectral signatures. They are also used in lasers, optical communications, and in the production of holograms.

How can diffraction gratings be used to improve the resolution of images?

By using a diffraction grating in front of a camera lens, the light from the scene is dispersed into its component wavelengths, which can then be captured separately on different parts of the camera's sensor. This allows for more detailed and accurate images, as the different wavelengths can be processed and combined to create a higher resolution image.

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