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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What happens to the intermediate images in Optics?

A common method to solve problems in optics for system of mirrors, surfaces with different refractive index, lens, slabs, mixture of mirror and lens etc. is to consider the image formed by the first ...
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How might I calculate the trajectory/deflection of a light beam near Schwarzschild and Kerr black holes?

Suppose I have a light beam (or a photon), with origin $\mathbf{o}$ and ray direction $\mathbf{d}$, and a Schwarzschild/Kerr black hole at the origin with Schwarzschild radius $r$, such that $||\...
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Image from a concave mirror with an inclined object [closed]

I have a line inclined 45º as the image below shows (the mirror is concave): The image will be virtual, enlarged and tends to infinity. I want to draw the image from that object. Can anyone help me?
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Which is more accurate, a quantum gyroscope or ring laser gyroscope?

I can't find any source which says whether quantum or laser gyroscopes are more accurate. I'm also wondering what the advantages and disadvantages are of each technology.
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How do I compute a Mueller matrix for a refracted ray?

When I consult most resources, I get a set of equations for Fresnel reflection and transmission which look like this: $$ r_\text{s} = \frac{n_1 \cos \theta_\text{i} - n_2 \cos \theta_\text{t}} ...
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Is rainbow formed in front or behind of a water droplets?

Single water droplet gives rise to formation of only a small part of rainbow. Is that part formed in between observer and droplet or behind the droplet and not between them?
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Why is the number of light rays refracted from a transparent media more than the number of reflected rays?

I came across a question related to the multiple image formation from a thick mirror due to partial refraction and reflection. It was asked that which image would be the most intense? In the solution ...
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Spatial Resolution and pixel smear and camera devices

Can anyone recommend a good source (video, textbook, online course) that I can use to learn more about spatial frequency, exposure, pixel smear, how cameras work. I only have some basic optical ...
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How far away does a taller object have to be in order to appear below eye-level?

A thought experiment between a friend and I. Let's say I'm 6ft tall, and I have a friend who's 7ft tall. To keep things very simple for the sake of discussion, we're on a flat level plane, and I have ...
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Intuitive Explanation behind algebraically adding the vertical shifts produced by transparent objects

Given are two transparent slabs of different refractive indexes, a point object is placed at the bottom of $B$. My book says that the total shift produced is the algebraic sum of the shifts of each ...
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Optics of Vehicle Convex Mirrors

I recently got in an argument with a friend while I was driving. When I moved to a different lane, I did not turn my head to check for any vehicles in my blind spot. Instead, how I checked was by ...
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Why do the eyes of a person wearing glasses not look blurry if almost everything looks blurry when I wear them?

When I wear my mother's (hyperopic) glasses, almost everything appears blurry, (the reason for which was explained in this answer). What I don't understand, is why this doesn't work backwards. ...
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How can the image be any size orher than the object?

Am image is just the set of images of all the points on the thing. The complete image has to be the same size as the object if there is exactly one image for each point on the object forming it. So an ...
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Proof of Snell's law [duplicate]

Snell's law states that $n_1 \sin i = n_2 \sin r$ where $i$ is the angle of incidence, $r$ is the angle of incidence and the refractive index, $n = \frac{c}{v}$ where $v$ is the velocity of the light ...
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Galilean telescope magnification coefficient?

So I've seen the magnification coefficient of the compound concave telescope to be $\frac{f_0}{f_e}$, but what is the magnification coefficient in the case of the convex galilean telescope? This may ...
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Generation of an beam with an arbitrary initial profile

Is it possible to generate a beam with an arbitrary initial profile? For example, the finite Airy beam has an initial profile $$\phi(s,0)=exp(\alpha s)Ai(s).$$ In practice, this finite Airy beam is ...
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Real or false image formation of a plane mirror and lens [closed]

If an object is placed in-between a plane mirror and a convex lens. Would the image that results from the reflection off the plan mirror into the lens be real. Rough diagram: Plane mirror------Object--...
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Studying curved mirrors. It's given that focal length equals half radius of curvature for concave spherical mirror, yet calculations show else

It is my first time studying reflection and the book states that for a concave spherical mirror, reflected rays parallel to the principal axis, $R$, pass through the focal point and the distance of ...
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Mathematical definition and notation of Fermat's Principle for least time

I was going through geometrical optics as it's a part of my undergrad course ,and I found about the Fermat's principle. The principle was understood but the mathematical equation given for it was not ...
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Deriving the thin lens formula from the lens maker formula

I've been studying refraction recently, and I faced some doubts regarding the thin lens approximation. The thin lens formula is given as : $$\frac{1}{v}-\frac{1}{u}=\frac{1}{f}$$ However, I also know ...
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Why angle of refraction parallel to base of triangle in triangular prism? [duplicate]

My textbook says that: At minimum deviation of a triangular prism, the refracted ray is parallel to the base of the triangle But I feel like it's only possible if the triangle is isosceles or ...
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How can solve to calculate position of image for any random point and random paraxial rays?

I am a high school student and I have a confusion related to optics {image formation via spherical mirrors) in all my books they say to find location of image its convenient to use the following rays&...
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How does one derive Fermat's principle of Least Time? [duplicate]

Fermat's principle states that the path taken by a ray between two given points is the path that can be traveled in the least time. I understand that Fermat's principle of Least time is crucial in ...
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What is optical path length? Does it make sense that the optical path length is variable or zero?

I've encountered an exercise where L(A,B) = sum of other OPLs that are parts of itself, and at the end we got that L(A,B) = 0?! But the definition is that L(A,B) = OPL = sum(...) = n×AB, so that means ...
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Is it possible to find the magnification of multiple lenses if the object is at infinity?

I understand the ray diagram of three lenses (converging, diverging, converging not stuck together) with an object at infinity, but is it possible to calculate the magnification of the entire system? ...
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Angle of Prism?

The definition of angle of prism is, "The angle formed due to two lateral faces of the prism is known as the angle of prism". My question is if there is an isosceles prism then which angle ...
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Reverse Vector Snell's Problem

Is there a simple way to reverse the Snell's-Equation-in-Vector-Form problem? I.e., given the incident and transmitted vectors $\,\mathbf{i}\,$ and $\,\mathbf{t}\,$ (both with norm = 1), find the ...
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Spherical mirrors or parabolic mirrors?

I am a high school student and have learnt about how curved surfaces reflect and refract (in "ray optics"). We were always told that these surfaces were spherical in shape, meaning they were ...
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Derivation in ray optics

How to derive the formula for magnification in spherical mirrors and thin spherical lenses? I already know the relationship between image distance (v), object distance (u) and focal length (f), in ...
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How to measure a 90 degree angle in a tilted image?

I look at an object through a microscope, which is not perfectly laying on the ground. I take a picture of it and try to measure if the object geometry has exactly 90 degrees at one of its edges. But ...
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How a hypermetropic person or a normal human eye see object placed beyond Focus of convex lens?

In our class it is taught that if you want to correct a hypermetropia , $u=-25 \ \mathrm{cm}$ and $v= \mathrm{near \ point \ of \ that \ person}$ But we knew , convex lens produce virtual image only ...
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How our eye see real images formed by pinhole camera? [duplicate]

How do we(eye) see real image form in pinhole camera? 1.Are rays that are forming image pass through screen and reach our eye help us too see it ? OR Light rays from hole from where we are looking at ...
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Is it possible to shape magnetic fields? [duplicate]

Is it possible to shape or focus magnetic fields like an optical lens does with light?
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How can there be 2 values for $x$?

The question is as follows : Find the value(s) of $x$ such that the object and the final image coincide. The object is at 'O'in a medium whose refractive index is 1. Now when I solved this, I got ...
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What should be the direction of the shift from the slab in this case?

Above is an image of a question, given by my teacher in which I had been asked to find the distance of the final image from the observer (Indicated by an eye). So here is what I understand, rays from ...
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Apparent error in Snell-Descartes' law in the case of refraction - what am I missing?

The law of refraction says that $$n_1\sin \theta_1=n_2\sin\theta_2$$ So we deduce that when $n_1<n_2$, we have $i_1>i_2$ and the refracted ray will be drawn closer from what is normal. If we ...
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Why image formed in concave mirror appears wrong when light rays come from focus and center of curvature or parallel to it? [duplicate]

I found a problem were my calculations doesn't match with geometric drawing. I have an object placed at a position half of the focal legth of a concave mirror. I had drawn an image similar to one ...
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Why do we consider the optical path length constant in a Cartesian Oval

I admit that this was from a homework question, but I'm having huge trouble wrapping my head around why the optical path length needs to be the same for a Lens that focuses every single ray emanating ...
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Simulate a camera PSF?

Say I have a $3D$ object stored as a $3D$ $\texttt{NumPy}$ array in python. I want to view this $3D$ object as a camera would give: a particular aperture, focal length, etc. My understanding is I can ...
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What is meant by longitudinal vision position In the phenomenon of apparent shift of an object due to refraction?

I was studying the topic " Apparent shift of an object due to refraction " and found a note in my study package - whenever the observer is not in the longitudinal vision position then the ...
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Where is the optical centre of a Concavo convex lens?

I have been taught that the Optical Centre of a lens is the point at the principal axis of a thin lens through which Ray of light passes undeviated. I was under the impression that it always passes ...
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Real image of virtual object

Are real images always inverted, even for a virtual object? I tried to make ray diagrams for such a situation in concave mirror, I am getting a real but erect and diminished image between pole and ...
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Representation of optical abberations in the different pulse propagation equations

Usually focusing a gaussian beam with a single lens can result in several optical abberations, such as spherical abberation. How are these abberations (if at all) represented in the common propagation ...
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Is a point object in optics really a point?

I am a high school student and I am a little confused about a thing I know generally when we say point object we meant that the size of the object is very small compared to the distance we are looking ...
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Using Snell's law in transmission and reflection coefficients

If we have an electromagnetic wave propagating between two media with refractive indices $n_1$ and $n_2$. The reflection and transmission coefficients at the interface can be written from `Optics, ...
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Why are all reflected rays concurrent?

Let us take a point object (real ) for simplicity . Irrespective of where object is located an image is always formed (virtual or real ,at finite distance or at infinite distance ) . So i wanted to ...
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What exactly is a "smooth surface" in geometrical optics?

Often in elementary optics, one considers so-called "smooth surfaces" (this is to be viewed in contrast with the idea of a "rough surface"), with plane mirrors being a prototypical ...
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Angular aperture of diverging beam after passing through a diverging lens

Consider an optical set-up as shown in the plot below: A light source, e.g. a laser diode, of diameter $d$ ($\approx$ 1 mm, but numbers are unimportant) is emitting a divergent beam having a half ...
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Details of how we see and percieve objects and images

I am a high school student and I have a question related to the concept of object and image I know where incident rays intersects this point is called object but here if this is the case here what ...
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Why is the equation governing image formation in reflection of mirrors and refraction of lenses the same?

From this article by physics classroom, we see that mirror equation is just: $$ \frac{1}{v} + \frac{1}{u} = \frac{1}{f}$$ With magnification: $$ m = \frac{- d_i}{d_o}$$ And in this article for ...

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