Improving Optics Accuracy with Digital Filtering and Ray Interpolation

[aspodkfpo]

Homework Statement

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Relevant Equations

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Just wondering whether it is actually possible to do this question accurately enough for it to basically look similar. Personally my diagram for the lines drawn in bold in the first diagram are slightly to the left compared to their diagram, by like 1cm on the x-axis, and in the second graph I do not have any of their ---\__ bumps.

If possible, how do you do this accurately, or is this one of those questions that are marked with leniency?

 

[berkeman]

Homework Statement:: n/a
Relevant Equations:: n/a

View attachment 267910

Just wondering whether it is actually possible to do this question accurately enough for it to basically look similar. Personally my diagram for the lines drawn in bold in the first diagram are slightly to the left compared to their diagram, by like 1cm on the x-axis, and in the second graph I do not have any of their ---\__ bumps.

If possible, how do you do this accurately, or is this one of those questions that are marked with leniency?

>Homework Statement:: n/a

It's kind of hard to answer your question without knowing what the problem statement is. Are you supposed to plot the intensity on the bottom of the pool for the instantaneous snapshot of the waves on the surface of the pool and the insolation angle as shown?

 

[aspodkfpo]

>Homework Statement:: n/a

It's kind of hard to answer your question without knowing what the problem statement is. Are you supposed to plot the intensity on the bottom of the pool for the instantaneous snapshot of the waves on the surface of the pool and the insolation angle as shown?

We get the light-black lines on the first diagram and are then required to plot what is shown as the bold lines in the answers.
From the lines in the first graph, we make inferences and plot the second graph of intensity.

 

[berkeman]

We get the light-black lines on the first diagram and are then required to plot what is shown as the bold lines in the answers.
From the lines in the first graph, we make inferences and plot the second graph of intensity.

In that case I think your 2nd plot is reasonable. The light from the sun is not coherent, so the intensity is just a function of how much light is getting concentrated where (by the ripples/waves on top of the pool surface). You can see this in real life in pools, BTW...

https://image.shutterstock.com/image-photo/empty-swimming-pool-on-bright-260nw-1406531447.jpg

 

[etotheipi]

It's always going to be a bit shaky here, since you're given a discrete number of lines and are asked to plot a continuous intensity curve.

A good start might be to determine intensity in the form $\text{rays}\,\,\text{cm}^{-1}$, i.e. just count how many rays strike between each of the pairs of markings on the axes. That will give you something quite spiky, since lots of intervals have no rays striking, so I think you'll just have to use your best judgement.

 

[aspodkfpo]

In that case I think your 2nd plot is reasonable. The light from the sun is not coherent, so the intensity is just a function of how much light is getting concentrated where (by the ripples/waves on top of the pool surface). You can see this in real life in pools, BTW...

https://image.shutterstock.com/image-photo/empty-swimming-pool-on-bright-260nw-1406531447.jpg

View attachment 267912

Just to clarify, the second diagram is the answers not mine. Mine did not have the double humps at 21 and 27, rather it looked like a quadratic curve. Was wondering whether that is accurate enough?

 

[berkeman]

In that case I think your 2nd plot is reasonable.

Just to clarify, the second diagram is the answers not mine.

Oh, no wonder it looks reasonable!

A good start might be to determine intensity in the form , i.e. just count how many rays strike between each of the pairs of markings on the axes. That will give you something quite spiky, since lots of intervals have no rays striking, so I think you'll just have to use your best judgement.

I agree (and this is probably what you did). You can then apply some lowpass digital filtering to your plot to smooth out the spikes and get closer to the answer plot. You could also try to interpolate more rays from the surface coming down to give you less spiky data to start with before applying your DSP LPF.

 

[etotheipi]

You can then apply some lowpass digital filtering to your plot to smooth out the spikes and get closer to the answer plot. You could also try to interpolate more rays from the surface coming down to give you less spiky data to start with before applying your DSP LPF.

That's very cool, I'd never heard of this technique before! There's some juicy details on the general theory here which I really enjoyed reading. Though dare say you'd probably have a hard time doing this during an olympiad