Reflection Diffraction Gratings

[JamesGman]

My lecturer has given me this formula for reflective diffraction

m landa = d (cos a - cos b)


where

m is order #
landa is wavelength
d is slit seperation
a is angle of inicdence
b is angle of reflection


The problem I have is I wasn't given any justification of this and have no idea where it comes from

 

[neu]

$$\lambda$$ = "lambda"

Do you mean this set up?
http://en.wikipedia.org/wiki/Diffraction#Diffraction_from_an_array_of_narrow_slits_or_a_grating

If so then I am sure your eq simplifies to the wiki eq: $$m \lambda = d sin \theta$$ is the incident angle is zero.

But check this, i haven't

 

[astrokreng]

or how it is derived. Can you explain this formula for me?

Sure, I'd be happy to explain this formula for you. First, let's define some terms:

- Order #: This refers to the order of the diffraction pattern, with the first order being the central peak and higher orders being the subsequent peaks on either side.
- Wavelength (λ): This is the distance between two consecutive peaks or troughs in a wave.
- Slit separation (d): This is the distance between the individual slits in a diffraction grating.
- Angle of incidence (a): This is the angle at which the incident light strikes the diffraction grating.
- Angle of reflection (b): This is the angle at which the reflected light exits the diffraction grating.

Now, let's look at the formula itself: mλ = d(cos a - cos b). This formula is known as the grating equation and it explains the relationship between the different variables in a reflective diffraction grating.

Essentially, this formula tells us that the wavelength of the diffracted light (mλ) is equal to the slit separation (d) multiplied by the difference between the cosine of the incident angle (a) and the cosine of the reflection angle (b).

But where does this formula come from? It is derived from the principles of diffraction and the geometry of a diffraction grating. When light is incident on a diffraction grating, it is diffracted into different orders depending on the wavelength of the light and the spacing of the slits. This can be seen as the different colored bands in a rainbow when light passes through a prism.

By applying the principles of diffraction and the geometry of the grating, we can derive the grating equation to explain the relationship between the different variables. This formula is widely used in scientific research and practical applications, such as in spectrometers and other optical instruments.

I hope this explanation helps you understand the formula better. If you have any further questions, please don't hesitate to ask your lecturer or reach out to me for clarification. Keep up the curiosity and good luck with your studies!