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Diffraction grating = a system which comprises of a vast number of narrow equally spaced parallel
slits. dSin = n
White light through a diffraction
grating, at each order maximum a
spectrum is formed due to different
colours having different wavelengths.
As red is longest wavelength it will
diffract more than blue, hence why it is
on outside of pattern.
Waves propagating from slits A B C interfere with one another, the
points of constant constructive interference is due to each subsequent wave having moved relative
to the previous one by exactly one wavelength, i.e. have a constant phase relationship. And are
This situation is the same for
greater angles of diffraction,
producing further maximum
orders (constructive interference
Further, to calculate the maximum
order (or total number of
diffracted orders seen), = 90,
so dsin90 = n as sin90=1. d=n.
So maximum order, n = d/. For n,
ALWAYS ROUND DOWN (even
Derivation of the equation:
dSin = n
Imagine each order as a right angled triangle:
Where the base is length D (distance from grating
to screen) and height is x (distance between
adjacent orders), the angle = in the main
So for this right angled triangle, tan = x/D
Using this idea, the equation is derived as:
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Here's a taster:
In the example above, using simple trigonometry where sin = o/h.
We can use the sides of the triangle equivalent.
i.e. Opposite, o = n. Hypotenuse, h = d
So getting sin = n / d, which rearranges to dsin = n
Note that in this example, as it's the 2nd order maximum, d is doubled as its the distance
between A and C not just A and B, and n would equal 2.…read more