Calculating the Number of Lines on a Diffraction Grating

In summary: The highest order spectrum which may be seen with monochromatic light of wavelength 600nm by means of a diffraction grating with 5000 lines/cm is the third order spectrum.
  • #1

Homework Statement


A diffraction grating gives a second-order maximum at as angle of 31° for violet light (λ = 4.0 × 10^2 nm). If the diffraction grating is 1.0 cm in width, how many lines are on this diffraction grating?

Homework Equations


d = (m)(λ)/sinθm

The Attempt at a Solution


d = (m)(λ)/sinθm
d = (2)(4.0 x 10-7 m)/sin(31°)
d = 1.6 x 10 x 10-6 m

0.01 m / 1.6 1.6 x 10 x 10-6 m = 6250 lines

Many thanks in advance! :smile:
 
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  • #2
You need to use the equation ## m \lambda=d \sin{\theta} ## for the location ## \theta ## of an interference maximum. From this equation and the info they gave you, you can compute "d"=the distance between the lines on the grating. (The grating is filled with these lines. Item of interest=your computed "d" is going to be very small=on the order of a wavelength of light.) The width of the grating is w=1.0 cm so you need quite a large number N of these closely spaced lines to make 1.0 cm. Do you know what the letter "m" represents?
 
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  • #3
EmilyBergendahl said:

The Attempt at a Solution


d = (m)(λ)/sinθm
d = (2)(4.0 x 10-7 m)/sin(31°)
d = 1.6 x 10 x 10-6 m

0.01 m / 1.6 1.6 x 10 x 10-6 m = 6250 lines

Is this what you mean? I was in the process of editing as you posted.
 
  • #4
Yes. Your d=1.6 E-6 (meters) is what it should read. I believe your answer is correct N=6250 but I would need to doublecheck the arithmetic. (And your m=2 is correct.)
 
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  • #5
Yes, whoops, got a little overzealous with the scientific notation there, haha.

Thank you Charles! :smile:
 
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  • #7
Zeynep Celik said:
why is m = 2?
In the statement of the problem in the OP (original post=post 1), it states that it is a "second order maximum" that they are observing. Thereby ## m=2 ## in the equation ## m \lambda=d \sin{\theta} ##.
 
  • #8
Charles Link said:
In the statement of the problem in the OP (original post=post 1), it states that it is a "second order maximum" that they are observing. Thereby ## m=2 ## in the equation ## m \lambda=d \sin{\theta} ##.
didn't notice that, thanks!
 
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  • #9
What is highest order spectrum which may be seen with monochromatic light of wavelength 600nm by means of a diffraction grating with 5000 lines/cm

I need answer for this question pls help me.
 

1. How do you calculate the number of lines on a diffraction grating?

The number of lines on a diffraction grating can be calculated by dividing the distance between the grating's rulings (also known as the grating spacing) by the wavelength of the light source. This calculation is known as the grating equation: N = d/λ, where N is the number of lines, d is the grating spacing, and λ is the wavelength of light.

2. What is the grating spacing?

The grating spacing refers to the distance between the parallel rulings on a diffraction grating. This distance is typically measured in millimeters (mm) or micrometers (μm) and is a crucial factor in determining the number of lines on the grating.

3. How does the number of lines on a diffraction grating affect the diffraction pattern?

The number of lines on a diffraction grating directly affects the diffraction pattern by determining the angle at which the diffracted light will be observed. As the number of lines increases, the angle of diffraction also increases, resulting in a wider diffraction pattern.

4. Can the number of lines on a diffraction grating be changed?

The number of lines on a diffraction grating is a fixed characteristic of the grating and cannot be changed. However, different gratings can have different numbers of lines, which can be chosen based on the desired diffraction pattern and experimental conditions.

5. How does the wavelength of light affect the number of lines on a diffraction grating?

The wavelength of light is a crucial factor in calculating the number of lines on a diffraction grating. As the wavelength increases, the number of lines also increases. This means that longer wavelengths of light will require a grating with a lower number of lines, while shorter wavelengths will require a grating with a higher number of lines to produce the same diffraction pattern.

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