What Is the Path Length Difference for Light in a Double Slit Experiment?

[Foxhound101]

Homework Statement

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.

Homework Equations

r=dsin(theta)
(theta)_m = m*(lambda/d)
y=L*tan(theta)

y_m = (m*lambda*L)/d

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.

 

[alphysicist]

Hi Foxhound101,

Homework Statement

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.

Homework Equations

r=dsin(theta)
(theta)_m = m*(lambda/d)
y=L*tan(theta)

y_m = (m*lambda*L)/d

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

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.