# Improving Optics Accuracy with Digital Filtering and Ray Interpolation

• aspodkfpo
In summary: 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...
aspodkfpo
Homework Statement
n/a
Relevant Equations
n/a

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?

aspodkfpo said:
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?

berkeman said:
>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.

aspodkfpo said:
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.

berkeman said:
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 said:
In that case I think your 2nd plot is reasonable.
aspodkfpo said:
Just to clarify, the second diagram is the answers not mine.
Oh, no wonder it looks reasonable!
etotheipi said:
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
berkeman said:
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

berkeman

## 1. What is the definition of "optics question's legitimacy"?

The term "optics question's legitimacy" refers to the validity and reliability of a question or problem related to optics, which is the branch of physics that deals with the behavior and properties of light. It is important to ensure the legitimacy of optics questions in order to accurately understand and analyze the principles and phenomena of light.

## 2. How do you determine if an optics question is legitimate?

An optics question can be considered legitimate if it is based on established principles and theories of optics, and if it can be tested and verified through experimentation or mathematical calculations. It should also be relevant and applicable to real-world situations.

## 3. What are some common mistakes that can make an optics question illegitimate?

Some common mistakes that can make an optics question illegitimate include using incorrect or outdated information, making assumptions that are not supported by evidence, and oversimplifying complex concepts. It is important to thoroughly research and understand the topic before formulating an optics question.

## 4. Are there any resources available to help determine the legitimacy of an optics question?

Yes, there are various resources available such as textbooks, scientific journals, and online databases that provide information and examples of legitimate optics questions. It is also helpful to consult with experts in the field of optics for guidance and clarification.

## 5. Why is it important to ensure the legitimacy of optics questions?

Ensuring the legitimacy of optics questions is crucial for accurate and meaningful scientific research and understanding. Illegitimate questions can lead to incorrect conclusions and hinder the progress of scientific knowledge. Furthermore, legitimate optics questions can help us to better understand the world around us and potentially lead to technological advancements.

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