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Light beam question

by nophun6
Tags: beam, light
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nophun6
#1
Jun1-06, 09:59 PM
P: 29
Q: The grating equation tells you at what angles different colors of light will appear: d sin θ = mλ
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,
λ is the wavelength (with the same length units as d), and
θ is the angle at which light with wavelength λ 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 = 1150 nm. Show the angles for red and blue light for m = 0, +1, and 1 by drawing them in appropriate colors


I am confused on how to start this problem. Suggestions on starting points are appreciated.
Thanks.
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andrevdh
#2
Jun2-06, 02:23 AM
HW Helper
P: 1,454
Since the wavelengths for the two colours are not given you should choose your own, maybe use [itex]\lambda_{red}=700\ nm,\ \lambda_{blue}=\ 500\ nm[/itex], and then work the diffraction angles out for the various orders for each of the two colours. It seems this is more a qualitative than quantitative question in spite of the given grating spacing.
tyco05
#3
Jun3-06, 08:49 AM
P: 161
It does seem more like a qualitative question... however, you are given enough information to solve for the diffraction angles.

You know:

d*sin(theta) = m*lambda

You are given (if you choose your blue and red wavelengths as Andre suggested) all variables except theta.

It's a matter of transposing the equation so that you have:

theta = something (it's up to you to work this out)

and then applying it three times for each wavelength (m= 0 , +1 and -1)

With this information, you can draw an accurate sketch, you should have 3 blue lines and three red lines....


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