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White Light Diffraction

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White light strikes a diffraction grating (540 lines/mm) at normal incidence. What is the longest wavelength that forms a third-order maximum?

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We have grating law:
(a + b) Sin (theta) = n * lambda
where a + b = grating element
theta = angle of diffraction with maximum value ...

Solution Summary

This solution uses grating law and shows complete calculations and answer.

See Also This Related BrainMass Solution

Optical Spectroscopy: Grating Equation, angular seperation for different colours.

This question is about the dispersion of light when passes trough a grating. the student asked for an illustration of angular seperation between two colours.

1. The grating equation tells you at what angles different colors of light will appear:
d sin = m

where d is the separation between the lines on the grating,
m is an integer (i.e., m = 0, 1, 2, 3, etc.) known as the diffraction order number,
is the wavelength (with the same length units as d), and
is the angle at which light with wavelength is diffracted.

Make a sketch based on the figure below to show a narrow parallel beam of white light shining onto a grating with line separation d = 1000 nm. Show the angles for red and blue light for
m = 0, +1, and -1 by drawing them in appropriate colors.

Answer: we can assume that the wavelength corresponding to blue is 450 nm and for blue let it be 650 nm.
For a given value of m, according to the equation given in the question
d sin = m
If , , which corresponds to , This is true for both Blue and red colour. So the re is no dispersion occurs.
For ( First order spectra)

, let , where , the angle corresponds to blue and is the angle corresponding to red.
By substituting the value of , for red and for blue. Substituting the values in the equation

Fom that =26.74 degree( right side of the normal line )
, degree(( right side of the normal line )

For the , we can write =-26.74 degree( left side of the normal line ) and ( left side of the normal line ).
The figure follows.

Please note that in the figure, I just shown the angular separation.

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