Young's Photon Interference - Question on Angle & Voltage

[Athenian]

Homework Statement

Convert the x-axis from volts (output in the file from the micrometer) to radians using the full-scale voltage (1 V) and full scan distance of the micrometer, and the distance from the double slit to the scanning slit in front of the detector.

Relevant Equations

Fraunhofer 1-slit Diffraction Equation:

$$I(\theta) = I_0 \Bigg[\frac{\sin\big(\frac{\pi a}{\lambda}\big) \sin(\theta)}{\frac{\pi a}{\lambda}}\Bigg]^2$$

Fraunhofer 2-slit Diffraction Equation:

$$I(\theta) = 4I_0 \cos^2 \bigg(\frac{\pi d}{\lambda} \sin(\theta) \bigg) \Bigg[\frac{\sin\big(\frac{\pi a}{\lambda}\big) \sin(\theta)}{\frac{\pi a}{\lambda}}\Bigg]^2$$

After conducting the photon interference experiment, below is a sample data of what we got:

Time (s)	Angle (V)	Two-slit Diode (V)
0​	0.988​	0.203​
0.102​	0.984​	0.297​
0.805​	0.976​	0.398​
1.201​	0.974​	0.5014​
1.31​	0.968​	0.526​

The above list goes on for quite a few columns. That said, what I cannot understand is why is the angle in - I assume - volts? How am I supposed to change it to radians? In the homework statement, I provided what I think may be the "hint" to get the angle to radians. But, to my limited understanding, I am somewhat confused at how one can go from volts to radians.

With the above data chart, I am supposed to create a "light intensity ($\mu$W) vs. angle (rad)" graph. However, I am not quite understanding how the above data can help me find the values for "light intensity (in microwatts)" and "angles (in radians)".

That said, I did just go straight ahead and graph out a "two-slit diode (V) vs. angle (V)" graph and it did come out to have a standard "diffraction graph" (the one with a lot of waves). Perhaps I am onto something here?

Ultimately, for those who are able to help me, thank you very much.

 

[Steve4Physics]

Homework Statement:: Convert the x-axis from volts (output in the file from the micrometer) to radians using the full-scale voltage (1 V) and full scan distance of the micrometer, and the distance from the double slit to the scanning slit in front of the detector.
.
.
After conducting the photon interference experiment, below is a sample data of what we got:

Time (s)	Angle (V)	Two-slit Diode (V)
0​	0.988​	0.203​
0.102​	0.984​	0.297​
0.805​	0.976​	0.398​
1.201​	0.974​	0.5014​
1.31​	0.968​	0.526​

The above list goes on for quite a few columns. That said, what I cannot understand is why is the angle in - I assume - volts? How am I supposed to change it to radians? In the homework statement, I provided what I think may be the "hint" to get the angle to radians. But, to my limited understanding, I am somewhat confused at how one can go from volts to radians.

With the above data chart, I am supposed to create a "light intensity ($\mu$W) vs. angle (rad)" graph. However, I am not quite understanding how the above data can help me find the values for "light intensity (in microwatts)" and "angles (in radians)".

That said, I did just go straight ahead and graph out a "two-slit diode (V) vs. angle (V)" graph and it did come out to have a standard "diffraction graph" (the one with a lot of waves). Perhaps I am onto something here?

Ultimately, for those who are able to help me, thank you very much.

You need to provide a diagram clearly showing the experimental setup. For example, there are 2 voltages in your table – you need to show where these come from.

There is too much missing information to answer you without lot’s of guesswork (at least for me). For example, what time is being measured in the ‘Time’ column of the table?

If you don’t get any helpful answers, I suggest you need to provide much more information.

 

[Athenian]

@Steve4Physics, thank you for your response.

The "time" column, to my understanding, refers to the time that transpired since the photo-multiplier tube (i.e. detector) detected the incoming photons. Therefore, if I were to extend the time column by - for example - 100 columns, you would only see the numerical values go continuously higher (e.g. from 1 to 100 seconds). In other words, "time" really just refers to the start and end of the experimentation.

As far as information goes, I believe this is all the material provides (beyond the background lesson).

Regarding the experimental setup, I did find a Google image that matches the experiment setup I was working with.
https://www.google.com/search?q=two...DypaYDA&bih=754&biw=1536#imgrc=FZnm1-IoDSgdTM

 

[kuruman]

Disclaimer: This is only a guess.
There is a slit in front of a light detector.
The slit and detector are moved across a double-slit interference.
The output of the detector in Volts is a measure of the light intensity from zero to whatever it is at the central maximum.
The motion of the slit is perhaps controlled by an electromechanical device that produces an output signal (0-1V) that is proportional tot he position of the slit. This is the voltage that needs to be converted to an angle in radians.

To @Athenian: You are provided with a hint about how to do this in the problem statement. You are told that the full scan distance of the micrometer corresponds to 1 Volt. You need to measure with a ruler or some such instrument the full scan distance. If it is, say, 10 cm then you will know that your conversion factor is 0.1 cm/V. You can then multiply all the voltages by the conversion factor to get distances on the screen. To convert to radians, you use the standard expression $$\tan\theta =\frac{x}{L}~\Rightarrow~\theta=\arctan\left(\frac{x}{L}\right)\approx \frac{x}{L}$$where $L$ is the distance from the double-slit to the detector and $x$ is the distance from the central maximum to the point of interest. The small angle approximation for $\theta$ most likely applies in your case.

 

[Steve4Physics]

@Steve4Physics, thank you for your response.
Regarding the experimental setup, I did find a Google image that matches the experiment setup I was working with.
https://www.google.com/search?q=two...DypaYDA&bih=754&biw=1536#imgrc=FZnm1-IoDSgdTM

Looking at your link, I agree with @kuruman.

Note, in your table:
1) The time column is irrelevant and should be removed.
2) The next column should be labelled ‘Micrometer output (V)’.
3) The next column should be labelled ‘Detector output (V)'.

The angle can be found as described by @kuruman. The intensity (in μW) can not be found unless you know the collection area and detector sensitivity. I suggest using the detector voltage values and calling them ‘Relative Intensity’ (no units) on the graph's 'y-axis'.

On a point of terminology, the table you posted has 3 columns (vertical) but 6 rows (horizontal). Don’t use the word ‘column’ when you mean ‘row’ or it will cause confusion!

 

[Gordianus]

The first formula quoted in the OP is wrong; it should be:$$I=I_0 \frac{\sin^2(\delta)}{\delta^2};\delta=\frac{\pi a\sin(\theta)}{\lambda}$$

 

[Athenian]

Steve4Physics and Kuruman, thank you so much for your help and clarifications!

For Steve4Physics: My apologies for the odd interchangeable use of rows and columns. Nonetheless, it is a lesson learned. Thank you!

For Gordianus: You are right! I did accidentally write the equation incorrectly. Thank you for catching that!