OPTICS: finding image position using matrix methods

In summary, the conversation is about a question that asks for an analytical solution to finding the position of an image produced by a concave mirror using matrix methods. The person asking the question is struggling to find resources and is hoping for guidance in the right direction. Suggestions are made to use transfer matrixes for translation and reflection to find the image position.
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Homework Statement



Hello! The question I'm looking to solve is asking me to "analytically evaluate the image" produced by a concave mirror (which I'm assuming is telling me to use matrix methods to find image position, though I'm not sure). I've come across matrix methods which give me the distance from the optical axis to where an incident ray crosses the input plane of the system, but I'm wondering what steps to take in order to find image position.

I haven't been to class is a few days and so I'm really quite lost, and not being able to find any resources which are consistent with this course is really frustrating. Hopefully someone can steer me in the right direction...

Thank you!
 
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Welcome to PF;
user_ said:

Homework Statement



Hello! The question I'm looking to solve is asking me to "analytically evaluate the image" produced by a concave mirror (which I'm assuming is telling me to use matrix methods to find image position, though I'm not sure).
That's not what the term "analytically" means - no.
It just means the answer should be an analytical solution rather than a numerical one.
Related to "closed form expression".

Thus you should find a closed-form expression for the position.

OTOH: it sounds like your coursework is covering matrix optics right now.

I've come across matrix methods which give me the distance from the optical axis to where an incident ray crosses the input plane of the system, but I'm wondering what steps to take in order to find image position.

Sketch the situation for ray diagrams - what is special about the image position?
Can you describe the special quality as something you can find from the matrix formalism.

I haven't been to class is a few days and so I'm really quite lost, and not being able to find any resources which are consistent with this course is really frustrating. Hopefully someone can steer me in the right direction...[/QUOTE]
Google for "matrix optics" or "ray transfer matrix".

If the light ray is represented by vector (y,y'), then it goes from the object position o to the mirror, gets reflected, and comes back to the viewer position. At some point the rays appear to diverge from a position other than the object.

So why not start with the transfer matrixes for translation and reflection?
 
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FAQ: OPTICS: finding image position using matrix methods

What is "OPTICS" and what does it involve?

"OPTICS" is a branch of physics that deals with the behavior and properties of light, including its interactions with matter. This field involves studying the properties of light, such as its wavelength and speed, as well as how it is affected by different materials and environments.

What are matrix methods and how are they used in optics?

Matrix methods are mathematical techniques used to analyze and calculate the behavior of light in optical systems. They involve using matrices, which are arrays of numbers, to represent the properties of light and the materials it travels through. These methods are used to find the position and properties of images formed by lenses, mirrors, and other optical elements.

Why is it important to find the image position in optics?

Finding the image position is important in optics because it allows us to predict and control the behavior of light in optical systems. This information is used in various applications, such as designing optical instruments, improving image quality, and understanding the behavior of light in different materials.

What are some common techniques for finding image position using matrix methods?

Some common techniques for finding image position using matrix methods include the paraxial ray tracing method, the Gaussian optics method, and the ABCD matrix method. Each of these techniques has its own advantages and limitations, and the choice of method depends on the specific optical system being analyzed.

What are some real-world applications of image position analysis using matrix methods?

Image position analysis using matrix methods has numerous real-world applications, including designing and optimizing optical systems for cameras, telescopes, and microscopes. It is also used in the development of optical sensors, laser systems, and fiber optics communication networks. Additionally, matrix methods are used in the analysis of eye disorders and in the design of corrective lenses.

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