Diffraction grating, distances between maxima

In summary: You should use the tangent directly.In summary, the question is asking for the separation on a screen between the second-order maxima for two different wavelengths of light passing through a grating with a line density of 1010 cm−1. To find this, one could calculate the angular spread of the second-order maxima for each wavelength and then take the difference between those two values. This would give the angular distance between the two maxima, which could then be converted to a vertical distance on the screen using the equation y = L tan(θ).
  • #1
TheKShaugh
22
0

Homework Statement



A grating has a line density of 1010 cm−1, and a screen perpendicular to the ray that makes the central peak of the diffraction pattern is 2.5 m from the grating. If light of two wavelengths, 590 nm and 680 nm, passes through the grating, what is the separation on the (flat) screen between the second-order maxima for the two wavelengths?

Homework Equations



[tex]dsin\theta = m \lambda[/tex]

The Attempt at a Solution



I thought I would find the angular distance to the second order maxima covered by each wavelength:

[tex]\theta = arcsin(\frac{2 \lambda}{d})[/tex] where d is [tex]\frac{1}{1010}\times 10^{-2}[/tex]

Then I would take the difference, and plug it into the equation [tex]sin\theta = \frac{y}{L}[/tex] and solve for y. This gives me the wrong answer but I don't see why this wouldn't work. Can anyone see my mistake?

Thanks!
 
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  • #2
TheKShaugh said:

Homework Statement



A grating has a line density of 1010 cm−1, and a screen perpendicular to the ray that makes the central peak of the diffraction pattern is 2.5 m from the grating. If light of two wavelengths, 590 nm and 680 nm, passes through the grating, what is the separation on the (flat) screen between the second-order maxima for the two wavelengths?

Homework Equations



[tex]dsin\theta = m \lambda[/tex]

The Attempt at a Solution



I thought I would find the angular distance to the second order maxima covered by each wavelength:

[tex]\theta = arcsin(\frac{2 \lambda}{d})[/tex] where d is [tex]\frac{1}{1010}\times 10^{-2}[/tex]

Then I would take the difference, and plug it into the equation [tex]sin\theta = \frac{y}{L}[/tex] and solve for y.

Take the difference of what?
You have two wavelengths, two angles and two y positions. You need the separation between the positions, that is, the difference of the y-s.
 
  • #3
ehild said:
Take the difference of what?
You have two wavelengths, two angles and two y positions. You need the separation between the positions, that is, the difference of the y-s.

What I meant was that I would solve for the angular spread of the second order maxima for one wavelength, then the other, and the take the difference of those two values. What I get should be the angular distance between the two maxima. I could then use the equation I gave in my OP and solve. This gives the same answer that I got: [tex]2.5sin(7.896)-2.5sin(6.845)[/tex] The idea is that if I calculate the angle to one maxima, I should be able to tell what vertical distance it covers. Then I can do the same for the other maxima, and take the difference between those two distances as the distance from one maxima to another.
 
  • #4
It is a good method, what result did you get? In principle, the distance of the maximum from the centre is L tan(θ). If θ is really small, the sine and the tangent are nearly equal. But the angles you got are not small enough.
 

Related to Diffraction grating, distances between maxima

1. What is a diffraction grating?

A diffraction grating is a device that is used to separate light into its component wavelengths by diffracting the light as it passes through a series of parallel slits or grooves on a reflective surface.

2. How does a diffraction grating work?

When light passes through a diffraction grating, it is diffracted by the slits or grooves on the surface. This causes the light to spread out into a spectrum, with the different wavelengths being diffracted at different angles.

3. What is the distance between maxima in a diffraction grating?

The distance between maxima, also known as the grating spacing, is the distance between adjacent slits or grooves on a diffraction grating. It is typically measured in micrometers (μm) or nanometers (nm).

4. How is the distance between maxima calculated?

The distance between maxima is calculated using the equation d*sinθ = m*λ, where d is the grating spacing, θ is the angle of diffraction, m is the order of the maximum, and λ is the wavelength of light. This equation is known as the diffraction grating equation.

5. What factors affect the distance between maxima in a diffraction grating?

The distance between maxima in a diffraction grating is affected by the grating spacing, the angle of diffraction, the order of the maximum, and the wavelength of light. Additionally, the number of slits or grooves on the grating and the type of material used can also affect the distance between maxima.

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