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roam
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Homework Statement
I have some difficulty understanding a part of the following problem:
In Young’s experiment, narrow double slits 0.20 mm apart diffract monochromatic light onto a screen 1.5 m away. The distance between the 5th minima on either side of the zeroth-order maximum is measured to be 34.73 mm. Determine the wavelength of the light.
Homework Equations
Here is a diagram of the double slit experiment:
http://imageshack.us/scaled/landing/850/doubleslit.jpg
Condition for minima: ##d \ \sin \theta = (m+\frac{1}{2}) \lambda##
Linear positions measured along the screen: ##\tan \theta = \frac{y}{L}##
##\therefore \ y_{dark} = \frac{L (m+\frac{1}{2})\lambda}{d}##
The Attempt at a Solution
So, in the question what is meant by "distance between the 5th minima on either side of the zeroth-order maximum"? I'm not sure if I understand this.
Does this mean the distance from the 5th minima on one side of the maxima to the 5th minima on the other side like this:
http://imageshack.us/scaled/landing/706/52496318.jpg
Did I understand the question correctly? If this is correct, then
##34.73=2y \implies y=17.37 \ mm##
And I can find the λ by rearranging the above equation:
##\lambda=\frac{y \ d}{L(m+\frac{1}{2})} = \frac{(17.365\times 10^{-3})\times (0.2 \times 10^{-3})}{1.5(5+\frac{1}{2})} = 4.2096 \times 10^{-7}##
Is this correct? The answer looks reasonable (about 420.96 nm in the blue/violet region of spectrum), but I doubt it is correct. Any help would be greatly appreciated.
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