# Problem: Plastic Covering One Slit in Double Slit Experiment

• chipwhisperer
In summary: The phase shift is because the light waves have different frequencies when they reach the plastic, causing a difference in the phase of the light waves.
chipwhisperer

## Homework Statement

A very thin sheet of plastic (n = 1.45) covers one slit of a double-slit apparatus illuminated by 570 nm light. The center point on the screen, instead of being a maximum, is dark. What is the (minimum) thickness of the plastic?

## Homework Equations

Constructive Interference:
d *sin(theta)=m*lamda

Destructive Interference:
d *sin(theta)=(m+1/2)*lamda

lamda_n=lamda/n

## The Attempt at a Solution

So I'm a TA for a physics class and I'm a little stumped on explaining this problem. The solutions manual says that the phase shift must be an odd multiple of one half. I got that. However, it then proceeds to write down this equation:

N= t/lamda_n - t/lamda = 1/2

where t is the thickness of the plastic. Any idea how they got this relation? I would really appreciate an explanation.

Thanks!

t = N lambda right.
What does N represent?

number of what??

N equals the phase shift I believe, i.e. 1/2, I'm not exactly sure though

chipwhisperer said:
So I'm a TA for a physics class and I'm a little stumped on explaining this problem. The solutions manual says that the phase shift must be an odd multiple of one half. I got that. However, it then proceeds to write down this equation:

N= t/lamda_n - t/lamda = 1/2

where t is the thickness of the plastic. Any idea how they got this relation? I would really appreciate an explanation.
Well, that expression is the phase difference between the two beams that converge at the center, expressed in terms of wavelengths. (lambda is the wavelength of light in air (or vacuum), where n = 1; lambda_n is the wavelength of light in the plastic, which is lambda/n.) The physical path lengths are the same; the only difference is that one passes through a thickness of plastic (phase shift = t/lamda_n) while the other beam passes through the same thickness of air (phase shift = t/lambda).

Okay, I get that. But, why is the phase shift = t/lamda? I just don't see that direct correspondence.

chipwhisperer said:
But, why is the phase shift = t/lamda?
If a lightwave travels from points A to B, do you not agree that the phase of the light at B differs from the phase it had at A? And that the phase shift in moving from A to B can be expressed by the number of wavelengths contained in the distance between A and B? For example, if the distance A-to-B is 1/2 lambda, when the light reaches B it is exactly 180 degrees out of phase compared to its phase when at A?

Let me know if this makes sense so far.

## 1. What is the purpose of using a plastic covering on one slit in a double slit experiment?

The purpose of using a plastic covering on one slit in a double slit experiment is to block or reduce the amount of light passing through that particular slit. This allows for the experiment to be conducted with only one slit open, providing a clearer and more precise pattern for analysis.

## 2. How does the plastic covering affect the interference pattern in a double slit experiment?

The plastic covering on one slit in a double slit experiment causes a decrease in the intensity of the light passing through that specific slit. This results in a decrease in the overall visibility of the interference pattern, making it easier to observe and analyze the pattern without any overlapping or confusing patterns.

## 3. Can the plastic covering be placed on either slit in a double slit experiment?

Yes, the plastic covering can be placed on either slit in a double slit experiment. However, it is important to note that the placement of the plastic covering will affect the interference pattern and the results of the experiment. It is recommended to place the covering on the slit with the highest intensity of light passing through it.

## 4. How does the thickness of the plastic covering impact the results of a double slit experiment?

The thickness of the plastic covering plays a critical role in the results of a double slit experiment. Thicker coverings will block more light, resulting in a decrease in the overall intensity of the interference pattern. This can make it easier to observe and analyze the pattern. However, if the covering is too thick, it may completely block the light and result in no interference pattern at all.

## 5. Can the plastic covering be replaced with another material in a double slit experiment?

Yes, the plastic covering can be replaced with another material in a double slit experiment. However, it is important to ensure that the material used has similar properties to the plastic covering and does not significantly alter the amount of light passing through the slit. This is important in maintaining the integrity and accuracy of the experiment's results.

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