Diffraction gratings and intensity

In summary, the conversation is about finding the wavelength of light using an interference pattern on a screen 1.0m behind a 950 lines/mm diffraction grating. The equation d sin(theta) = m(lambda) is used and the small angle approximation of replacing sin(theta) with y/L is also mentioned. The person attempting the solution is having trouble and realizes they forgot to find sin(theta) before plugging in the variables.
  • #1
Deneb Cyg
10
0

Homework Statement



The interference pattern in this image:
http://session.masteringphysics.com/problemAsset/1074248/3/22.P45.jpg
is seen on a screen 1.0m behind an 950 lines/mm diffraction grating.

What is the wavelength of the light? (expressed in nanometers to 2 sig figs)

Homework Equations



I know that the equation relating the variables is: d sin(theta)=m(lambda) where theta is the angle from the center maximum to the mth maxima. d being the distance between slits in the grating.

And using the small angle approximation I think you can replace sin(theta) with y/L where y is the distance between the central maximum and the mth one and L is the distance of the screen from the grating

The Attempt at a Solution



I tried plugging the variables into the equation but I can't seem to get the right answer.

ie:
d(y/L)=m(lambda)
(1/950000)(.436/1)=1lambda
lambda=460nm which is wrong

What am I doing wrong?
 
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  • #2
0.436/1 is tanθ. Find sinθ
 
  • #3
Thank you. That worked. I can't believe I missed that.
 

FAQ: Diffraction gratings and intensity

What is a diffraction grating?

A diffraction grating is an optical component that consists of a periodic structure with a large number of parallel and equidistant lines or slits. When light passes through a diffraction grating, it splits into its component wavelengths, creating a rainbow-like spectrum.

How does a diffraction grating affect the intensity of light?

A diffraction grating can affect the intensity of light by causing constructive and destructive interference. When light passes through the grating, the waves from each slit interfere with each other, either amplifying or canceling each other out. This results in bright and dark fringes in the diffraction pattern, with the brightest fringes corresponding to constructive interference.

What factors affect the intensity of the diffraction pattern?

The intensity of the diffraction pattern is affected by the wavelength of light, the distance between slits in the grating, and the angle of incidence. Longer wavelengths will produce wider fringes, while shorter wavelengths will produce narrower fringes. Increasing the distance between slits will decrease the distance between fringes, and changing the angle of incidence will shift the location of the fringes.

What is the difference between a transmission and reflection diffraction grating?

A transmission diffraction grating allows light to pass through the grating, while a reflection diffraction grating reflects light off its surface. Transmission gratings are typically used for spectroscopy, while reflection gratings are more commonly used in optical instruments such as telescopes.

What applications use diffraction gratings?

Diffraction gratings have a wide range of applications, including spectroscopy, laser systems, optical communications, and astronomy. They are also used in various scientific instruments, such as spectrometers, monochromators, and wavelength filters. Diffraction gratings are also commonly used in everyday items, such as CD and DVD players, where they are used to separate the different colors of light to create images and data storage.

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