- #1
roam
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Homework Statement
I'm having some trouble understanding the following solved 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.
Solution:
Position of mth minima relative to central maximum is:
##(m-\frac{1}{2}) \lambda = a \ sin \theta =\frac{ay_m}{L} \implies y_m = \frac{L(m-\frac{1}{2})\lambda}{a}##
Distance on the screen between the 5th minima on either side of the central maximum is:
##\Delta y = y_5-y_{-5} = \frac{(4.5-(-4.5))L \lambda}{a} = \frac{9L \lambda}{a}##
##\therefore \ \lambda = \frac{\Delta y a}{9L} = 514 \ nm##
I don't understand why they have used ##(m-\frac{1}{2}) \lambda## as the condition for destructive interference, instead of ##(m+\frac{1}{2}) \lambda##?
Homework Equations
For destructive interference my textbook uses:
##d \ sin \theta_{dark} = (m+\frac{1}{2}) \lambda##
(this is an approximation)
The Attempt at a Solution
If I use -1/2, then 5th minima turn out to be are 9λ apart, just like the model answer.
However when I use +1/2 I get a totally different solution:
##\therefore \ \lambda = \frac{\Delta y a}{(5.5-(-5.5)) L}= \frac{\Delta y a}{11 L} =421 \ nm##
So, why do they use -1/2? And which method is correct?
Any help is greatly appreciated.