PHY C15: Diffraction Grating

On By irfansyahrilIn Physics, Study Notes

Last for the chapter!

  • Diffraction Grating
  • Equation: nλ = d sin θ
  • White light through a diffraction grating

Let’s go!

What is a diffraction grating?
A plate with a large number of closely spaced parallel slits.

Image result for diffraction grating

What happens when monochromatic light is sent through a diffraction grating?
A pattern of narrow bright fringes is formed.

This pattern is caused, once again, by interference of light waves.

What equation is used to describe the fringe pattern?

If you have sharp eyes, you’ll notice that this is similar to the equation used to describe single-slit interference.

HOWEVER, the purpose of this equation is DIFFERENT:
This describes the pattern of BRIGHT MAXIMA, not the minima in the equation for single-slit interference.

Full Proof:
https://www.khanacademy.org/science/physics/light-waves/interference-of-light-waves/v/diffraction-grating

How do you use this equation?

d = spacing between adjacent slits
θ = angle from centre line to maxima
n = order of maximum (0,1,2,3,…)
λ = wavelength of light

The 0th order maximum is the bright maximum at the centre, the 1st order maxima are the 2 maxima closest to the centre, etc.

Image result for diffraction grating pattern
This image uses ‘m’ instead of ‘n’ to denote the maxima, but it’s still accurate.
From HyperPhysics

Let’s try a classic example.
Given:

  • number of lines per metre = 5.00 x 105
  • 3rd-order maximum observed at an angle of diffraction of 78°

Find λ.

STEP 1:
Calculating d		If there are x lines per metre, the distance between the lines is 1/x*.

*Of course, it should be 1/(x-1) if you think logically, but since x is a very large number, it doesn’t make much of a difference.

In this case,
d = 1/(5.00 x 105)
STEP 2: Substituting the values into the equationundefined
STEP 3:
Finding λ		undefined

What happens when you send white light through a diffraction grating?
The different frequencies (colours) making up white light will be diffracted by a different amount, since they have different wavelengths.

Since violet & blue have the shortest wavelengths, they will have smaller angles.

Since red has the longest wavelengths, it has the largest angle.

It should look like this:

On the left side of the figure is a diffraction grating represented by a vertical bar with five horizontal slits cut through it. A single horizontal arrow, representing white light, points at the center slit from the left side. On the right side, five arrows spread symmetrically above and below the horizontal centerline. The arrow that is on the horizontal centerline points at a white block labeled central white. The first arrows above and below the centerline point to rainbow-colored blocks labeled first-order rainbow. The second arrows above and below the centerline point to slightly faded rainbow-colored blocks that are labeled second-order rainbow.
From Lumen Learning

A real-life image would look like this:

What’s an application of diffraction grating?
It can be used as a SPECTROMETER.

This is a tool used to identify the wavelength(s) of light that is sent through it.

⇐ Previous in Physics: Single Slit Interference
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