Diffraction Grating Problem ?

In summary, the conversation discussed the use of a diffraction grating with 10000 lines per cm to observe second order bright fringes using yellow light with a wavelength of 589 nm. The correct equation was given as d sin theta = m (λ), and the value of sin(theta) was calculated to be 1.178. However, the teacher pointed out that this number is larger than 1 and therefore does not represent a rational angle. The conversation also mentioned the need to substitute the wavelength in meters and the possibility that the grating constant may be 1000/cm instead of 10000/cm.
  • #1
Shahab Mirza
28
0
Hi,
1. Homework Statement
Q : A diffraction grating with 10000 lines per CM is illuminated by yellow light of wavelength 589 nm, At what angles is the 2nd order bright fringes seen ?

Homework Equations


From my textbook , I got this equation , d sin theta = m (λ)

The Attempt at a Solution


Ok so what I did was that I plugged values properly , i.e
sin theta = mλ/d
For second order , m=2 so,
= (2) (589 X 10nm) / (1/10000 X 1/ 100)

and the answer is 1.178 , but out teacher said that this number is larger than 1 and so sin theta does not represent any rational angle , so tell me that how to know that sin theta in this case "1.178" does not represent any rational number , please help me out with this , Thanks [/B]
 
Physics news on Phys.org
  • #2
What does 589x10 nm mean? You have to substitute the wavelength in meters.
The value you got for sin(theta) is correct, perhaps the grating constant is 1000/cm instead of 10000/cm. The grating constants are usually in the range of micrometers.
Your teacher is right, in case of such fine grating, the second maximum does not appear.
 
  • #3
ehild said:
What does 589x10 nm mean? You have to substitute the wavelength in meters.
The value you got for sin(theta) is correct, perhaps the grating constant is 1000/cm instead of 10000/cm. The grating constants are usually in the range of micrometers.
Your teacher is right, in case of such fine grating, the second maximum does not appear.

Thanks for reply Sir ,
Actually in real problem which I solved on a paper I wrote 1/10000 X 1/100 and converted it into right unit .
Thanks a lot for your kind reply .
 

1. What is a diffraction grating?

A diffraction grating is an optical component that consists of a large number of evenly spaced parallel lines or slits. It is used to separate and diffract light into its component wavelengths, allowing for the analysis of the spectral content of light.

2. How does a diffraction grating work?

A diffraction grating works by causing light to diffract or spread out as it passes through the parallel lines or slits. This creates a pattern of bright and dark spots, known as interference fringes, which correspond to the different wavelengths of light being diffracted.

3. What is the difference between a transmission and reflection diffraction grating?

A transmission diffraction grating allows light to pass through the grating, while a reflection diffraction grating reflects light off its surface. Both types of gratings can be used to diffract light, but they have slightly different properties and applications.

4. What factors affect the performance of a diffraction grating?

The performance of a diffraction grating can be affected by several factors, including the number of lines or slits per unit length, the spacing between the lines or slits, and the angle of incidence of the light. The material and quality of the grating can also play a role in its performance.

5. What are some common applications of diffraction gratings?

Diffraction gratings have a wide range of applications in various fields, including spectroscopy, telecommunications, and laser technology. They are used to analyze the spectral content of light, create optical filters, and produce lasers with specific wavelengths. They are also used in some types of display technology, such as 3D movies and holograms.

Similar threads

  • Introductory Physics Homework Help
Replies
3
Views
1K
  • Introductory Physics Homework Help
Replies
5
Views
1K
  • Introductory Physics Homework Help
Replies
5
Views
1K
  • Introductory Physics Homework Help
Replies
1
Views
6K
  • Introductory Physics Homework Help
Replies
3
Views
1K
  • Introductory Physics Homework Help
Replies
2
Views
2K
  • Introductory Physics Homework Help
Replies
10
Views
2K
  • Introductory Physics Homework Help
Replies
3
Views
5K
  • Introductory Physics Homework Help
Replies
4
Views
977
  • Introductory Physics Homework Help
Replies
8
Views
24K
Back
Top