Basic diffraction grating question

In summary: The grating is probably mislabeled.In summary, the conversation discusses the use of a diffraction grating with a claimed number of 13500 lines/inch to determine the number of lines per cm. The attempt at a solution involves using the grating equation and measuring the distance between the central and first maximum to calculate the number of lines per cm. The calculated value of 2080 lines/cm is significantly lower than the claimed value, suggesting that the grating may be mislabeled.
  • #1
Grebulous
3
0
This is an intro lab-based question.

Homework Statement


I took a 650 nm red laser and shined it through a diffraction grating that claimed it had 13500 lines/inch, which comes to 5315 lines/cm in civilized people units. The grating was placed 30 cm away from a piece of paper on the wall. The distance between the central maximum (m=0) and the m=1 maximum was measured to be 4.1 cm. I'm trying to verify that the number of lines per cm is in fact around 5315.

Homework Equations


The grating equation, d sin(theta) = m(lambda)

The Attempt at a Solution


m=1 for the first maximum, and rearranging the equation, d = lambda/sin(theta). d equals the spacing between each slit, which is just 1/N, where N is the number of lines per cm. sin(theta) is 4.1/sqrt(30^2 + 4.1^2) = 0.1354. So, N = sin(theta)/lambda = 0.1354/(6.5 x 10^-5 cm) = 2080 lines/cm, to 3 s.f.

I find that answer odd - did I make some really basic mistake, or does the grating really have 2.5 times fewer lines than it claims it does? If I were to go the other way and assume N was right, I'd get an ultraviolet wavelength, and I double-checked my measurements. Can anybody spot my goof?
 
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  • #2
Your calc looks good.
 

What is a diffraction grating?

A diffraction grating is an optical component that is used to separate light into its component wavelengths. It consists of a surface with closely spaced parallel lines or grooves that act as slits, causing diffraction of the light passing through it.

How does a diffraction grating work?

A diffraction grating works by causing diffraction of light as it passes through the closely spaced parallel lines or grooves on its surface. This results in the separation of the light into its component wavelengths, creating a spectrum.

What is the difference between a diffraction grating and a prism?

A diffraction grating and a prism are both optical components used to separate light into its component wavelengths. However, a diffraction grating uses multiple slits or grooves to create a spectrum, whereas a prism uses refraction to separate the light.

What are some applications of diffraction gratings?

Diffraction gratings have many applications in science and technology, including spectroscopy, optical instruments, lasers, and telecommunications. They are also used in many everyday items such as DVD players and barcode scanners.

How do you calculate the diffraction angle for a diffraction grating?

The diffraction angle for a diffraction grating can be calculated using the formula: θ = sin^-1 (mλ/d), where θ is the diffraction angle, m is the order of diffraction, λ is the wavelength of light, and d is the distance between the grooves on the grating.

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