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Lightpath length difference 
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#1
Sep2908, 03:25 PM

P: 52

1. The problem statement, all variables and given/known data
Two narrow slits are 0.12 mm apart. Light of wavelength 550 nm illuminates the slits, causing an interference pattern on a screen 1.0 m away. Light from each slit travels to the m=1 maximum on the right side of the central maximum. Part A  How much farther did the light from the left slit travel than the light from the right slit? Express your answer using two significant figures. 2. Relevant equations r=dsin(theta) (theta)_{m} = m*(lambda/d) y=L*tan(theta) y_{m} = (m*lambda*L)/d 3. The attempt at a solution I don't understand how to do these problems... theta_{m} = (m*lambda*)/d theta_{m} = (1*(5.5*10^7m)/(1m) theta_{m} = 5.5*10^7 path length difference = dsin(theta) so... r = d*sin(theta) r = 1m *sin(5.5*10^7) r = 9.599^9m r = 9.6nm That doesn't appear to be the correct answer(Unless MasteringPhysics is wrong). Sadly, I don't know if I did the right steps or used the correct equations. Any help is appreciated. 1. The problem statement, all variables and given/known data 2. Relevant equations 3. The attempt at a solution 


#2
Sep2908, 07:27 PM

HW Helper
P: 2,249

Hi Foxhound101,
[tex] \sin\theta=\frac{m\lambda}{d} [/tex] The approximation you are using ([itex]\theta=\frac{m\lambda}{d}[/itex]) is fine since the angle is small enough, but remember that this approximation is true if the angle is measured in radians. So the angle you found is [itex]5.5\times 10^{7}\mbox{ rad}[/itex]. 


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