Maxima of Diffraction Grating with 300 Lines/mm and Wavelength of 450 nm

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In summary, the problem involves incident light of wavelength 450 nm on a grating with 300 lines per millimeter. The equation d sin(theta) = n(lambda) is used to determine the number of orders of diffraction maxima, with m being an integer ranging from negative infinity to positive infinity. This results in a total of 15 possible diffraction maxima for the given conditions.
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Viviana
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Homework Statement



Light of wavelength 450 nm is incident normally on a grating with 300 lines per millimeter. How many orders of diffraction maxima can be obtained?



Homework Equations


d sin(theta) = n(lambda)

The Attempt at a Solution


300 lines per millimeter is 3.33 x 10^-6. And 450 nm should be 4.5 x 10^ -7 m.
This is my equation:
3.33 x 10^-6 sin 90 = n (4.5 x 10^ -7)
I get n= 7.4 = 7
The correct answer is 15. But i just can't get this answer. =( Can someone please guide me?
 
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  • #2
What is in the middle point, just opposite to the centre of the grating, minimum or maximum? And are maxima at one side only? What values can m have?

ehild
 
  • #3
Does that mean there are two maxima for each order?
 
  • #4
ehild said:
What is in the middle point, just opposite to the centre of the grating, minimum or maximum? And are maxima at one side only? What values can m have?

ehild

Maxima are at both sides. But i still don't know how to get values of m.
 
  • #5
Can you please give some more hints
 
  • #6
m is integer, including negative numbers and zero. So the farthest maxima are either at 90°or -90°.

ehild
 

FAQ: Maxima of Diffraction Grating with 300 Lines/mm and Wavelength of 450 nm

What is a diffraction grating?

A diffraction grating is a scientific tool used to separate light into its component wavelengths. It consists of a surface with many closely spaced parallel grooves or lines, which act as a series of small slits that diffract the light passing through them.

How does a diffraction grating work?

When light passes through a diffraction grating, the grooves or lines act as a series of parallel slits, causing the light waves to interfere with each other. This interference results in the splitting of the light into its different wavelengths, producing a spectrum.

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

A transmission diffraction grating allows light to pass through the grooves, while a reflection grating reflects the light off the surface of the grooves. Both types produce a diffraction pattern, but a transmission grating is typically more efficient at diffracting light.

What is the difference between a ruled and a holographic diffraction grating?

A ruled diffraction grating is made by physically cutting grooves into a surface, while a holographic grating is created using a laser to produce a pattern of interference fringes on a photosensitive material. Holographic gratings generally have higher resolution and are more precise than ruled gratings.

What are the applications of diffraction gratings?

Diffraction gratings are used in a variety of scientific and technological fields, such as spectroscopy, laser technology, and telecommunications. They are also commonly used in optical instruments such as spectrometers, monochromators, and telescopes.

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