How to improve the accuracy of Young's double slit experiment?

My teacher asked me to find the separation of a double slit by finding the distance between fringes. I wonder how I can reduce the experiment error. So what can I do?

What research have you done so far? What have you found out? What school level is this for?

phinds said:

What research have you done so far? What have you found out? What school level is this for?

Simple high school experiment. According to Δy=λD/a, where D is the distance between the screen and the double slit, Δy is the distance between fringes, λ is the wavelength of laser light, and a is the separation of the double slit. All variables except a are known. The aim of the experiment is to find out the value of a. I got an experiment result with an error of 3%. Can the error be further reduced?

Jason Ko said:

Can the error be further reduced?

Almost certainly, but first you will have to figure out where it is coming from. How accurate are your distance measurements? How confident are you that the wavelength is what you expect?

Nugatory said:

Almost certainly, but first you will have to figure out where it is coming from. How accurate are your distance measurements? How confident are you that the wavelength is what you expect?

The wavelength is told, it seems that the only error came from the measurement of Δy and D.

Jason Ko said:

The wavelength is told, it seems that the only error came from the measurement of Δy and D.

And how are they being measured? By what instruments exactly, and what is the error/tolerance for those devices?

phinds said:

And how are they being measured? By what instruments exactly, and what is the error/tolerance for those devices?

simply ruler measured

Jason Ko said:

simply ruler measured

And you have not answered the most important question that I asked:

what is the error/tolerance for those devices?

This is like pulling teeth.

First, just because you get a 3% deviation between what you measure and "the back of the book" doesn't mean you have a 3% measurement. You might have a 10% measurement and just got lucky. Do you know everything in your equation to better than 3%?

Second, you need to look at every element in your equation foe the answer, and ask what you can do to measure it better. What happens if I make it bigger? Make it smaller? What limits are there to this - the distance to the screen might be a meter, and maybe 1/2 or 2 meters is possible, but a micton or a mile probably isn't. It's the result of that thought process that your teacher wants to see.

To be fair, if @Jason Ko is at high school (as implied) it's more than possible that he hasn't been taught what is needed for a decent error analysis. But yes, if you don't specify what instruments you used and what you did with them then we can't really help. And that applies to all requests for help! The more information you can provide (within reason) the less time we waste going backwards and forwards asking for it.

The things you need to think about are the errors you could have made on each measurement. You have three: the wavelength, the fringe spacing, and the grating-to-screen distance.

You say the wavelength was given to you. Ok, you can't really do anything to improve that result. You could have a look online and see if you can find typical wavelength variation for your source - if it's huge then you probably can't improve your accuracy much.

You say you used a ruler for everything else. How did you use it? What exactly did you measure? (Peak-to-peak distance? From a graph, or a photo, or on the live screen? Or something else entirely?) Did you use a metre rule and was the grating-to-screen distance more than a metre? How much error do you think there is in each measurement?

Ibix said:

To be fair, if @Jason Ko is at high school (as implied) it's more than possible that he hasn't been taught what is needed for a decent error analysis.

That is fair, but I don't see anyone proposing a full error analysis with quadrature addition and derivatives and the like either.

I think it is, however, well within what is expected of a high school student to say "if we make this change, we can potentially do a little better, but if we make this other change, we can potentially do a lot better - but if we do this third thing, it probably won't help."

A high school student should be able to answer the following: "If we presently use a HeNe laser as the light source, would the measurement improve if we used a green laser pointer? If so, by about how much?"

Jason Ko said:

I wonder how I can reduce the experiment error. So what can I do?

Try thinking out of the box. If someone asked you to measure the thickness of some sheets of paper, what could you do to get the best accuracy if all you had was a ruler with 1mm markings on it? Likewise if they asked you to find the spacing between threads on a bolt, what would be a 'good' strategy'? And why?