Solving Light Interference with 2 Slits - 550 nm, 0.12 mm Apart

[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?

Homework Equations

y_m = (m*lambda*L)/d
theta_m=lambda/d
r=d*sin(theta)

The Attempt at a Solution

So...
L=1*10^9nm
d=1.2*10^6nm
lambda=550nm
m=1

I have tried a few different things, but I have no idea as to correctly proceed. I have been sticking those numbers into the equations above, but I am not getting any good answers. I must be missing something obvious...

 

[anathema]

Thank you for your post. Based on the given information, we can calculate the distance traveled by the light from each slit using the formula r=d*sin(theta), where r is the distance traveled, d is the distance between the slits, and theta is the angle of diffraction.

In this case, the angle of diffraction can be calculated using the formula thetam=lambda/d, where lambda is the wavelength of light and d is the distance between the slits. Plugging in the values, we get thetam= 550nm/1.2*10^6nm= 4.58*10^-4 radians.

Now, using this value of theta, we can calculate the distance traveled by the light from each slit. For the light from the left slit, the distance traveled would be r=d*sin(theta)=1.2*10^6nm*sin(4.58*10^-4)= 0.55 nm. Similarly, for the light from the right slit, the distance traveled would be r=d*sin(theta)=1.2*10^6nm*sin(4.58*10^-4)= 0.55 nm.

Therefore, the light from the left slit traveled the same distance as the light from the right slit, which is 0.55 nm. This means that the light from the left slit did not travel farther than the light from the right slit.

I hope this helps. Let me know if you have any further questions.

 

[baba89]

I would like to first clarify that the unit of measurement for distance in the given information is in millimeters (mm), not nanometers (nm). This is important to note when using the equations for calculating interference patterns.

To solve for the distance traveled by light from the left slit compared to the right slit, we can use the equation ym = (m*lambda*L)/d, where ym is the distance from the central maximum to the mth maximum, lambda is the wavelength of light, L is the distance from the slits to the screen, and d is the distance between the slits.

First, we convert all the given measurements into meters to ensure consistency in units:
L = 1.0 m
d = 0.12 mm = 0.00012 m
lambda = 550 nm = 0.00000055 m

Substituting these values into the equation, we get:
ym = (1*0.00000055*1.0)/(0.00012) = 0.00458 m

This means that the distance from the central maximum to the first maximum on the right side is 0.00458 m. Since the slits are 0.12 mm (0.00012 m) apart, the light from the left slit must have traveled an additional 0.00458 m to reach the same point on the screen. Therefore, the light from the left slit traveled 0.00000446 m farther than the light from the right slit.

In summary, the distance traveled by the light from the left slit is approximately 0.00000446 m farther than the light from the right slit. This difference in distance is due to the path difference between the two slits, which is essential in creating the interference pattern on the screen.