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Light beam question 
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#1
Jun106, 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. 


#2
Jun206, 02:23 AM

HW Helper
P: 1,449

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.



#3
Jun306, 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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