Number of diffracted orders produced

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In summary, the conversation is about calculating the angle of diffraction and number of diffracted orders produced when a laser beam of wavelength 630nm is directed at a diffraction grating with 300 lines per millimetre. The formula used is d x sintheta = n x wavelength, with d being 1/300000 and n being 2. The first part of the calculation results in an angle of 22.2 degrees, while the second part yields 5.29 degrees, which differs from the book's answer. The person is seeking help and apologizing for posting on multiple forums.
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aurao2003
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Homework Statement


Hi
A liitle help will be appreciated. The question is as follows:
A laser beam of wavelength 630nm is directed normally at a diffraction grating with 300 lines per millimetre. Calculate:
a) The angle of diffraction of each of the first 2 orders
b) The number of diffracted orders produced



Homework Equations



I used the formula

d X sintheta = n x wavelength





The Attempt at a Solution


N= 300000
therefore d= 1/300000

n=2
Wavelength = 630nm

Putting the above value in I obtained 22 .2 degrees

b) For the second part, I surmised that theta = 90 degrees
Therefore,
n = d/wavelength

I obtained 5. 29. But this diifers from the books answer.

Please help!
 
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I've replied to this on TSR.
 
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lol! Apologies again. You could probably guess I post on a few forums. Please keep on tracking me. Its highly appreciated.
 

1. What is the meaning of "Number of diffracted orders produced" in the context of diffraction?

The "Number of diffracted orders produced" refers to the number of distinct diffraction patterns that are created when a wave (such as light or sound) encounters an obstacle or passes through a narrow slit. These patterns are created due to the interference of the waves and can be observed as bands of light or dark areas.

2. How is the number of diffracted orders produced related to the wavelength of the wave?

The number of diffracted orders produced is directly related to the wavelength of the wave. As the wavelength increases, the number of diffracted orders also increases. This is because longer wavelengths have a lower diffraction angle, resulting in more diffraction patterns being produced.

3. Can the number of diffracted orders produced be controlled?

Yes, the number of diffracted orders produced can be controlled by changing the size and shape of the diffracting object. For example, a smaller slit will produce fewer diffraction patterns while a larger slit will produce more. Additionally, the number of diffracted orders can also be affected by the angle of incidence and the type of wave (e.g. sound waves vs. light waves).

4. How does the distance between the diffracting object and the screen affect the number of diffracted orders produced?

The distance between the diffracting object and the screen can affect the number of diffracted orders produced. As the distance increases, the diffraction angle also increases, resulting in fewer diffraction patterns being produced. This is because the waves have more space to spread out and interfere with each other, causing the pattern to become more spread out and less defined.

5. What is the significance of the number of diffracted orders produced in experiments and real-world applications?

The number of diffracted orders produced is an important factor in various experiments and real-world applications. For example, in optics, the number of diffracted orders can be used to determine the properties of a material by analyzing the diffraction pattern. In diffraction gratings, the number of diffracted orders can also be used to create specialized filters and spectrometers. Understanding the number of diffracted orders produced is crucial in many fields such as physics, engineering, and chemistry.

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