# Light-path length difference

by Foxhound101
Tags: distance, light
 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) ym = (m*lambda*L)/d 3. The attempt at a solution I don't understand how to do these problems... thetam = (m*lambda*)/d thetam = (1*(5.5*10^-7m)/(1m) thetam = 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
HW Helper
P: 2,250
Hi Foxhound101,

 Quote by Foxhound101 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) ym = (m*lambda*L)/d 3. The attempt at a solution I don't understand how to do these problems... thetam = (m*lambda*)/d thetam = (1*(5.5*10^-7m)/(1m) thetam = 5.5*10^-7
Remember that this is really:

$$\sin\theta=\frac{m\lambda}{d}$$

The approximation you are using ($\theta=\frac{m\lambda}{d}$) 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 $5.5\times 10^{-7}\mbox{ rad}$.

 path length difference = dsin(theta) so... r = d*sin(theta) r = 1m *sin(5.5*10^-7) r = 9.599^-9m
This number was calculated with the angle measure set to degrees, not radians.

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