Diffraction gratings - calculating the highest order maximum

In summary, the conversation discusses the use of a diffraction grating with 2192 lines per centimetre to observe monochromatic light with a wavelength of 694 nm. The question asks for the highest order maximum that can be observed, and the equation dsinθ = mλ is used to solve for m. However, there is uncertainty about which angle to use for θ and it is pointed out that the given value for d seems too large for diffraction to occur.
  • #1
Marcargo
6
0

Homework Statement


Monochromatic light of wavelength 694. nm is incident on a diffraction grating with 2192 lines per centimetre. What is the highest order maximum that can be observed?



Homework Equations



dsinθ = mλ

The Attempt at a Solution



d = 2192/cm = 21.92/m
λ = 694 x 10 -9m
sinθ = ?

m = dsinθ/λ
= (2192 x sinθ)/(694 x 10-9

I think that this is the equation to use, but I'm not sure what angle to use. I initially tried 90 for θ, but then logically thinking about it, that wouldn't work as light travels only in straight lines. Not sure how to carry on from here. Some insight would help!

Thanks







n.b. Given answer = 6
 
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  • #2
What is the highest angle possible?

But I don't believe that value for d ... it's 11 orders of magnitude bigger than the wavelength!
You only get diffraction if d is comparable to the wavelength otherwise we'd see baseball diffraction around doorways.
 

1. 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 large number of parallel, equally spaced slits or grooves that are etched onto a flat surface. When light passes through the grating, it is diffracted and produces a spectrum of colors.

2. How are diffraction gratings used in scientific research?

Diffraction gratings are commonly used in scientific research, particularly in spectroscopy and astronomy. They are used to analyze the properties of light, including its wavelength and intensity. By measuring the diffraction patterns produced by a grating, scientists can gather information about the composition and structure of various materials and celestial objects.

3. What is the highest order maximum in a diffraction grating?

The highest order maximum in a diffraction grating refers to the highest order of diffraction that can be observed. This occurs when the angle of diffraction is at its maximum value, and all of the light passing through the grating is diffracted at this angle. This order is dependent on the spacing of the grating, the wavelength of light, and the angle of incidence.

4. How do you calculate the highest order maximum in a diffraction grating?

To calculate the highest order maximum in a diffraction grating, you can use the formula: m = d sinθ / λ, where m is the order of diffraction, d is the spacing of the grating, θ is the angle of diffraction, and λ is the wavelength of light. By rearranging this formula, you can solve for any of the variables to determine the order of diffraction.

5. Are there any other factors that can affect the highest order maximum in a diffraction grating?

Yes, there are several other factors that can affect the highest order maximum in a diffraction grating. These include the width of the slits or grooves, the thickness of the grating, and the refractive index of the material. Additionally, the quality of the grating and any imperfections in its construction can also affect the diffraction pattern produced.

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