Solving Diffraction Grating Homework: Max Wavelength at 11°

In summary, for a monochromatic plane wave normally incident on a diffraction grating with 105 lines/m, the visible wavelengths that would produce a maximum at 11° are 636 nm and 477 nm for m = 3 and m = 4, respectively. This can be found by using the equation d*sinθ = m*λ and solving for λ, where d = 1 x 10^-5 m and m is any whole number.
  • #1
Swan
16
0

Homework Statement


A monochromatic plane wave is normally incident on a diffraction grating with 105 lines/m. For what visible wavelengths would this grating produce a maximum at 11°.

Homework Equations


d*sinθ = m*λ


The Attempt at a Solution


d = 1 x 10-5 m

I don't get how to actually solve it because i don't know what the m for this situation would be.
 
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  • #2
Hi Swan! :smile:
Swan said:
For what visible wavelengths would this grating produce a maximum at 11°.

I don't get how to actually solve it because i don't know what the m for this situation would be.

(we usually use "n", not "m")

it can be any whole number …

there may be more than one value for which there is a solution :wink:
 
  • #3
tiny-tim said:
Hi Swan! :smile:


(we usually use "n", not "m")

it can be any whole number …

there may be more than one value for which there is a solution :wink:

Hello tiny-tim. Thank You for replying. How would i go about solving this question?
 
  • #4
by using your equation …

what do you get? :smile:
 
  • #5
tiny-tim said:
by using your equation …

what do you get? :smile:

I got at m = 3 and m = 4 the diffraction grating would produce a maximum at 11° at visible wavelengths of 636 nm, 477 nm respectively to m = 3, m = 4.
 

Related to Solving Diffraction Grating Homework: Max Wavelength at 11°

1. What is a diffraction grating?

A diffraction grating is a device that contains a large number of parallel, equally spaced slits or grooves that are used to separate light into its component wavelengths. It works by causing interference patterns of light, resulting in a spectrum of colors.

2. How is the maximum wavelength at 11° calculated?

The maximum wavelength at 11° is calculated using the equation λmax = d * sin(θ), where λmax is the maximum wavelength, d is the spacing between the grating grooves, and θ is the angle of diffraction. This equation is known as the grating equation.

3. What is the significance of finding the maximum wavelength at 11°?

Finding the maximum wavelength at 11° is important because it allows us to determine the resolving power of the diffraction grating. The higher the maximum wavelength, the better the resolving power, as it means the grating can separate light into a wider range of wavelengths.

4. How does the number of grooves on the diffraction grating affect the maximum wavelength at 11°?

The number of grooves on the diffraction grating has a direct relationship with the maximum wavelength at 11°. As the number of grooves increases, the maximum wavelength also increases, resulting in a higher resolving power for the grating.

5. Are there any other factors that can affect the maximum wavelength at 11°?

Yes, there are other factors that can affect the maximum wavelength at 11°, such as the angle of incidence, the width of the slits, and the quality of the grating. However, these factors are usually kept constant in order to accurately calculate the maximum wavelength using the grating equation.

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