Questions tagged [geometric-optics]

The subfield of optics in which light propagation is approximated in terms of rays. It mainly includes reflection and refraction on surfaces.

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Double slit followed by lens

If the focal length of the second lens is $ƒ$, prove that maxima are located at $y_m$, where $y_m = mƒ\frac{\lambda}a$. I have tried to use the equation of lens but I am not sure what should I put as ...
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Derivation of paraxial equation from textbook [closed]

I am currently reading the book "Modern Optical Engineering, 3rd Edition" and I am struggling to derive a specific equation. You can find the corresponding text snippet in the appendix (1, 2)...
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How Young was able to see diffraction pattern?

I am interested in how was young able to see diffraction pattern even though he used candle
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61 views

Why is it harder to use a white light source in a Michelson Interferometer?

In a Michelson Interferometer, a light beam is split into 2 different beams that travel different optical paths, through the "arms" of the interferometer. Then, they are reflected and, ...
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Proof: Line joining the image and the object is always perpendicular to the mirror [closed]

I tried to find a proof, but couldn't find one. Anyone knows?
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Magnification of a compound microscope

Whilst finding the magnification of a compound microscope, we multiply the linear magnification of the objective with the angular magnification of the eyepiece. This gives us the angular magnification ...
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Image formed by concave mirror due to rays which are parallel to each other but not parallel to the principle axis

I was recently revising Optics and out of nowhere the thought came to mind that what will happen if parallel rays are fallen on a concave mirror that make some angle with the principle axis......the ...
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Mathematical expression for refraction within a spherical lens

Qs: How do I show that for a point object, for a ray at a large angle from the optical axis, spherical aberration (SA) produces a distorted focal length $f_{SA}$ that is shorter than the normal focal ...
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Regarding measurements on traveling microscope

In a experiment with traveling microscope to determine thickness of a glass slab , what is the physical significance of the readings that we get from the vertical scale ?, Means What are two points ...
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Will this combination focus my image closer?

Bringing thin lens together changes their effective focal length. $$\frac{1}{f_{\text{eff}}}=\frac{1}{f_{1}}+\frac{1}{f_{2}}$$ Lets us consider a biconvex lens. If we cut it along the principal axis ...
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Answer different using effective focal length of combination of lens

Q)The figure shows a silvered lens. $\mu_A = 1.6$ and $\mu_B = 1.2$, $R_1 = 80$cm, $R_2 = 40$cm and $R_3 = 20$cm. An object is placed at a distance of 12 cm from this lens. Find the image position. I ...
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Magnification of an object at focal point

Why do I see an image when I place an object at a focal point of a lens? I've been tinkering around with a simple concave lens and my phone's LED. The lens has a focal length of about 5cm. When I ...
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Why don't I see infinite images with parallel mirrors? [duplicate]

Sitting on the barbershop, watching myself in the mirror which is parallel to another mirror (so that two mirrors are parallel to each other), I was seeing an infinite number of photocopies. After a ...
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Infinite sum of transmitted parallel light fields

I'm currently studying optics and came across the possibility of retrieving the original electric (light field) from a pair of partially reflecting mirrors, but I am confused by several ...
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Why does extinction efficiency, $Q_{\rm ext}$, in Mie theory approach 2 in the limit of large particles?

I'm having some conceptual trouble understanding the extinction efficiency, usually denoted as $Q_{\rm ext}$, in Mie theory. I know that $Q_{\rm ext} = Q_{\rm sca} + Q_{\rm abs}$ where $Q_{\rm sca}$ ...
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Spherical Lens Instead of Parabolic Lens

I know that using the paraxial approximation, spherical lenses behave like parabolic lenses. It seems that there is no reason to use spherical lenses instead of parabolic (because they are used in the ...
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Optical power collected by a detector coming from a Lambertian disk object in an active illuminated camera

I would like to estimate reduction of optical power in an active illuminated camera when a flat lambertian target is moved away from the camera. Below is formal description of the problem, I’m just ...
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39 views

What shape lens will focus parallel laser beams to the smallest point?

I'm playing with Algodoo optics. I'm trying to focus parallel lasers using refraction. I thought an ellipse or parabola would work, but not precisely. As you can see in this picture, the ellipse ...
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1answer
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Endpoints in Fermat's Principle

Are the endpoints of the light ray path in Fermat's principle must be fixed? To clarify my question: Using Wikipedia definition for Fermat's Principle: Fermat's principle states that the path taken ...
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Calculating Light Fall-Off From Large Source

"the inverse square rule is often still a useful approximation; when the size of the light source is less than one-fifth of the distance to the subject, the calculation error is less than 1%"...
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1answer
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Reflectors that reflect sunbeams to a certain point at any given time

Let us say you live in a town at a latitude of around 50 degree North. The town doesn't get much, if any, sun, because there are hill ranges to the east, to the south, and to the west. Inspired by ...
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Derivation of Fermat's Principle from the Least Action Principle [duplicate]

Can I prove that Fermat's Principle (i.e. that light beam travels between two points in the path that require minimum time) using the Least Action Principle for electromagnetic wave? (from analytical ...
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Law of reflection in vector form: how is $\vec{n}_2 = \vec{n}_1 - 2(\vec{n}_1 \cdot \vec{s}) \vec{s}$ derived?

I am told that the law of reflection can be stated in the following two parts: The angle of reflection is equal to the angle of incidence. The incident ray, the normal to the reflecting surface at ...
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$ABCD$ matrix formalism for concave mirror

I need to calculate the $ABCD$ matrix for a thick concave mirror, in the situation in which the light comes from the plane side of the mirror, and it is the concave part that is coated (for reference, ...
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33 views

Resolution power of the Bragg law

A physical system that follows the Bragg law of diffraction, for example an electron scatter, shows interference patterns at some angle that follows the equation $nλ = 2d\sin(θ).$ Usually just the ...
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Thin lens equation calculation does not match experimental value, why?

for an optics experiment I had to design a $2$-lens system to image a grating, the diagram looks like this: The focal length of both lenses is $15$cm, at the end of the system there's a camera ...
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Water Whirlpools - Why Uniform Shadow?

I was experimenting with creating shadows from not fully formed whirlpools, such as this one: The direction of the light was essentially from bottom to top in this image. I think I understand most ...
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Optical phenomena due to temperature gradient in the atmosphere

What kind of phenomena can we observe due to the deviation of the light in the atmosphere, for example when the reflection index vary with the altitude. I would say that the orange lights in the ...
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1answer
29 views

Reflection on moving mirrors [closed]

Say I have an endless mirror, in a x y plane, at y=1. Situation 1: the mirror is stationary and when we send light vertically from the origin, the light reflects back and returns to the origin. ...
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Resource suggestion for optics based on vectors

I'm looking for a book which develops concepts similar to the one discussed in this post.
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Spherical Aberrations from Concave Mirrors

I am trying to derive a general equation for a ray reflected from a concave mirror like so: I've started with a generic ray with the equation $y = h$ and a circle centered on the origin $x^2 + y^2 = ...
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Light traveling in glass transmitted through an air gap

Consider a plane wave traveling in glass incident on a small air-gap. The situation is illustrated below (reflected fields omitted) for arbitrary materials. My professor derived the expression for ...
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Ray Diagrams: Where is the eyepiece located in a reflector telescope?

I'm in the process of building my own reflector telescope; I have an 8" primary mirror with a focal length of 1200mm. Of course a telescope has a focuser that lets the eyepiece move up and down ...
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How to calculate magnification with a lens array?

I am studying plenoptic camera, I have a simple system with a main lens, a microlens array and a sensor. I am following Hahne thesis (http://www.plenoptic.info/) and I want to calculate the ...
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Why can I see my face in a spoon?

If I hold a spoon with the concave side facing me, it approximates a concave mirror. If my eye is symbolised with an arrow, then we can represent the situation like this: The problem then arises. The ...
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Do identical, equally spaced lenses possess the same magnification, or does it depend on the sample's distance?

Do identical, equally spaced lenses always have the same magnification, or does it depend on the sample's distance to the first lens? This question comes from trying to solve: "There are 4 ...
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Range of magnification outside plane of focus in a microscope

This should be a simple question, but somehow it's stumping me due to the way microscope objectives are, necessarily, built and classified (compared to, e.g., ideal thin lenses and photographic lenses)...
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Problem of lens distance - Geometrical optics

I'm study geometrical optics and I'm doing an exercise which says: To the left of a thin lens an object is located at a distance p in various positions, indicated in the table. For each of the ...
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1answer
46 views

Snell law with two unknowns [closed]

I having troubles with a basic geometric optics exercise which says: The image shows a glass block immersed in water ($n_\text{water}=1,33$). What it’s the refraction index $n_\text{glass}$ of the ...
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Convex Lens forming plane wavefront

As we can see in the above diagram, as we move along the symmetric axis of the convex lens, D varies. Therefore the rays coming out of the point source hitting different points of the lens surface ...
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Can the concept of optical étendue apply to sources at infinity?

The general expression of optical étendue is: $$dG = n^2 \, dS \, cos \theta \, d\Omega$$ Can the concept of optical étendue be reduced to a useful expression when considering a source at infinity (an ...
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What is the waist radius of a gaussian beam after passing through lenses with different numerical apertures?

I have a question regarding gaussian beams and lenses. If a collimated gaussian beam hits a lens with a certain numerical aperture ($\mathrm{NA}$), we can calculate the beam waist in the focus by $\...
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1answer
25 views

What is the meaning of the random surface realization , $\zeta (x,y)$, in optics?

When reading Terahertz Spectroscopy and Imaging, I came across the Kirchhoff Approximation on Rough Surface Scattering Approximations. It is stated that: "The scattered field from the Kirchhoff ...
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Variation of Optical density

How does the optical density of air vary with height. I know about variation of Optical density within smaller heights like that observed in phenomenon of Mirage and looming but when we are concerned ...
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What's the physical mechanism inside the distribution of slightly polarized refracted ray?

If we emit unpolarized light from a source on a plane surface at Brewster's angle $\theta_{B}$, then we get a fully polarized reflected ray and a slightly polarized refracted ray whereas $\theta_{B} = ...
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1answer
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What's the logic behind light's following the longest path according to Fermat's Principle? [duplicate]

In our textbook, it's written that light rays will follow the minimum or maximum distance after being reflected from the plane surface and thus the path will be fixed. At somewhere, I read that light ...
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1answer
53 views

How can I rearrange the exact sag equation? [closed]

I apologise if this is a basic question on a site such as this but my maths skills aren't the best. The exact sag equation is $s = r - \sqrt{(r^2 - y^2)}$. We are required to know in my module that ...
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A confusion related to optics

I am a high school student and I am a little confused about a topic, My confusion is that, (say an object is $1$ dimensional) I doubt optics while studying the formation of image what we do is take $2$...
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Is a virtual image always erect?

Is a virtual image always erect? If so why it can't be never inverted. I got this doubt because I can see my inverted image on the concave side of the spoon and we know that inverted images are real ...
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1answer
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What sign conventions are used here? Geometrical optics

I'm reading Theory and Problems in Optics By Eugene Hecht (Schaum's outline series). I'm not able to understand, What sort of sign convention are they using? It says, Table 4-1 summarizes the sign ...

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