Diffraction grating problem, missing orders, diffraction minimum and maximums.

In summary, missing orders occur in a diffraction grating when a diffraction minimum coincides with an interference maximum. This happens when d = 2D for all even orders (m=2,4,6), and when d/D = m1/m2 where m1 and m2 are integers. When d + D, the limit in which the space between slits becomes negligible, the equation for diffraction from a single slit must also be used.
  • #1
NCyellow
22
0

Homework Statement


Missing orders occur for a diffraction grating when a diffraction minimum coincides with an interference maximum. Let D be the width of each slit and d the separation of slits. (a) show that if d = 2D, all even orders (m=2,4,6) are missing. (b) show that there will be missing orders whever d/D = m1/m2. where m1 and m2 are integers. (c) Discuss the case d + D, the limit in which the space between slits becomes negligible.


Homework Equations


sin(theta) = m(lamda)/d


The Attempt at a Solution


I figured out that in order for there to be a missing order m1 and m2 needs to coincide. However, setting m1D=m2d (m2 can't be 0), plugging in the given information d=2D, I simply get m2=m1/2. That did not seem to prove anything. Please give me some hints.
 
Physics news on Phys.org
  • #2
You'll need to use the equation for diffraction from a single slit also.
 
  • #3


I would first start by understanding the concept of diffraction and how it relates to diffraction gratings. A diffraction grating is a device that consists of a large number of parallel slits or lines, which can diffract light into a spectrum of colors. When light passes through the slits, it diffracts in different directions, producing a pattern of bright and dark fringes on a screen.

The phenomenon of missing orders occurs when certain orders of diffraction are not observed in the diffraction pattern. This happens when a diffraction minimum coincides with an interference maximum, resulting in destructive interference and canceling out the corresponding order.

(a) To show that all even orders are missing when d = 2D, we can use the equation sin(theta) = m(lamda)/d, where m is the order of diffraction. For even orders (m=2,4,6), we can see that m(d/2) = mD, which means that the sine of the angle of diffraction will be equal to zero. This corresponds to a diffraction minimum, which coincides with an interference maximum, resulting in a missing order.

(b) For the general case of d/D = m1/m2, where m1 and m2 are integers, we can rearrange the equation to get m1D = m2d. This means that the diffraction minimum for order m1 coincides with the interference maximum for order m2, resulting in a missing order.

(c) When d is very small compared to D, the space between the slits becomes negligible. In this case, the equation sin(theta) = m(lamda)/d becomes invalid, as the distance between the slits cannot be neglected. This means that there will be no missing orders in this limit, as all orders of diffraction will be observed in the diffraction pattern.

In conclusion, the phenomenon of missing orders in diffraction gratings occurs when diffraction minima coincide with interference maxima. This can happen for different values of d/D, resulting in missing orders for certain values of m. However, when the space between slits becomes negligible, there will be no missing orders in the diffraction pattern.
 

1. What is a diffraction grating?

A diffraction grating is an optical component consisting of a large number of parallel, evenly spaced lines or slits that are used to separate light into its different wavelengths.

2. What are "missing orders" in a diffraction grating problem?

Missing orders refer to the absence of certain wavelengths or colors in the diffraction pattern produced by a diffraction grating. This can occur when the spacing between the lines or slits is not perfectly uniform or when there is interference from other sources of light.

3. What causes diffraction minimums and maximums in a diffraction grating?

Diffraction minimums and maximums occur as a result of constructive and destructive interference between the different wavelengths of light passing through the grating. The spacing between the lines or slits determines the angles at which these minimums and maximums occur.

4. How can you prevent missing orders in a diffraction grating problem?

In order to prevent missing orders, the diffraction grating must be carefully manufactured with precise and evenly spaced lines or slits. Additionally, the light source must be monochromatic and the grating must be properly aligned and oriented with respect to the light source.

5. What is the relationship between the number of lines in a diffraction grating and the number of diffraction orders that can be observed?

The number of diffraction orders that can be observed is directly proportional to the number of lines or slits in the diffraction grating. This means that the more lines there are, the more diffraction orders can be seen. However, the spacing between the lines also plays a role in determining the number of orders that can be observed.

Similar threads

  • Introductory Physics Homework Help
Replies
3
Views
1K
  • Introductory Physics Homework Help
Replies
10
Views
1K
  • Introductory Physics Homework Help
Replies
5
Views
1K
  • Introductory Physics Homework Help
Replies
1
Views
6K
  • Introductory Physics Homework Help
Replies
10
Views
2K
  • Introductory Physics Homework Help
Replies
2
Views
2K
  • Introductory Physics Homework Help
Replies
8
Views
24K
  • Introductory Physics Homework Help
Replies
3
Views
5K
  • Introductory Physics Homework Help
Replies
4
Views
969
  • Introductory Physics Homework Help
Replies
4
Views
1K
Back
Top