Geometrical optics, or ray optics, is a model of optics that describes light propagation in terms of rays. The ray in geometric optics is an abstraction useful for approximating the paths along which light propagates under certain circumstances.
The simplifying assumptions of geometrical optics include that light rays:
propagate in straight-line paths as they travel in a homogeneous medium
bend, and in particular circumstances may split in two, at the interface between two dissimilar media
follow curved paths in a medium in which the refractive index changes
may be absorbed or reflected.Geometrical optics does not account for certain optical effects such as diffraction and interference. This simplification is useful in practice; it is an excellent approximation when the wavelength is small compared to the size of structures with which the light interacts. The techniques are particularly useful in describing geometrical aspects of imaging, including optical aberrations.
We were studying reflection due to plane mirrors and our sir derived the relation between velocity of image and velocity of object in case of a plane mirror. He took the following case as bare for deriving the formula.
Following is the detailed working
Now I was wondering if I could derive it...
Let there be a sphere whose inner surface consists of a perfectly reflecting surface.
It has a hole on it which allows a ray of light to enter.
Give the angle made with the normal of the hole when the ray of light enters such that the probability
that the ray comes out is the least?Assuming the...
Homework Statement
I read that the magnification for a point object is undefined, but when we draw ray diagrams we consider the rays to be emanating from a point source and also define magnification for it- what am I missing?
Homework Equations
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The Attempt at a Solution
(conceptual query)
Homework Statement
I needed help to undestand some concepts in Ray Optics for my assignment. The topics which U am concerned are: Part 1: Mirror Equation, Refraction at singly curved surface, lens maker's equation, combination of thin lenses in contact.
Part 2: Magnification Power of simple...
the largest telescope in the world has an aperture of 10 m. According to the fresnel distance this makes ray optics valid for it, for a wavelength of lightsay 500 nm, uptil a distance of 2 * 10^7 m. I have read that after the fresnel distance, diffraction tends to dominate. But telescopes tend...
Hello,
I would like to reduce the beam size of a laser by a factor of 10, with the purpose of replacing a long (750 mm) lens with a more compact design.
Ideally I'd make a Galilean lens pair where the ratio of the focal lengths are 10:1 to produce a small collimated beam. However, I think I...
Homework Statement
Consider an optical tweezer operated in the ray optics regime as shown in Figure. Net reflection angle of the ray shown in Figure is θ = 10◦ (See Figure). Since more photons take the thick ray than the thin ray, a net force of F = 1 pN is exerted on the sphere toward the...
Hi everybody,
I’m trying to calculate the shape of a boundary line f(x) between two mediums that collimates rays from a point light source. This requires the rays to hit the boundary line under a certain angle, so I calculated the slope m(φ) of the boundary line for a ray with polar angle φ (φ...
Fairly simple question I'd like someone to help with please. My teacher has me confused so I figured I'd turn to the forums for help.
1. Alright, so in an exam we had a ray diagram to draw. "Complete the ray diagram shown in Figure 6" they said (I sketched a replica * thumbs up*...
Homework Statement
The mirror in the image below deflects a horizontal laser by angle θ. What is the angle φ if θ = 60°.
Homework Equations
θi=θr
The Attempt at a Solution
So I know that, if I draw a line normal to the mirror, that will make it so that the incident angle and the reflected...
Homework Statement
You wish to use a converging mirror to form an image that is N times larger than the object. R is the radius of curvature of the mirror. At what distance o from the mirror should you place the object? Determine the object distance. Express your answer in terms of N and R...
In most (perhaps all) books it was mentioned that intersection of the light from the object when reflected by the mirror or refracted by a lens intersect at a particular point. That point when traced till the principal axis gives the image. (Provided object lies on the axis). I do not understand...
Alright I was doing some basic questions on ray optics when this doubt came to my mind
So my doubt goes like this:(IT may be silly)
Consider a concave mirror with pole P and centre of curvature C
Its principal axis is extended on both sides
Now consider a ray parallel to the principal axis
Call...
I am trying to follow the derivation of lens maker's formula from the textbook "University Physics", p.1133 (https://books.google.com.hk/books?id=nQZyAgAAQBAJ&pg=PA1133#v=onepage&q&f=false )
I can understand the first equation because it is just the object–image relationship for spherical...
Homework Statement
http://i.imgur.com/q6EaspT.png
2. The attempt at a solution
why is the answer C? shouldn't the aperture in front of the screen create a shadow that blocks all the light except the rays that go through slit? (the width of the slit is >>>1mm so it won't make a diffraction pattern.)
Homework Statement
Basically, derive the formula ## m = \frac{ 25 cm}{f_e} \frac{L}{f_o} ## using ray matrices. This just has variable tube length and assumes eye to object distance is 25 cm.
Homework Equations
Ray matrices: ## \left[ \begin{array}{cc} 1 & d \\ 0 & 1 \end{array} \right] ##...
Its an often prøven fact that a convex lens focused rays parallel with the optical axis into the focal point of the lens, but what about rays that are parallel with each other and with a small angle to the optical axis?
In ray diagrams with telescopes (such like the one below) one often draws...
Homework Statement
A light ray parallel to the x-axis strikes the outer reflecting surface of a sphere at a point (2,2,0). Its center is at the point (0,0,-1). The unit vector along the direction of reflected ray is ##x\hat{i}+y\hat{j}+z\hat{k}##. Find the value of ##yz/x^2##.
Homework...
Hi friends,
Please help me in answering this problem
The problem is as follows,
https://fbcdn-sphotos-e-a.akamaihd.net/hphotos-ak-prn1/s480x480/11130_2937865262994_1085043361_n.jpg
Well,
Friends when the lower mirror would be at position 'A', which is moving in the upward direction...
Hi friends,
Please help me in answering this problem
The problem is as follows,
https://fbcdn-sphotos-g-a.akamaihd.net/hphotos-ak-ash3/s480x480/557923_2937818221818_1718139220_n.jpg
Well,
As far as I am concerned, When white light fall on the first surface, after refraction...
Homework Statement
A 1.0-cm-tall object is placed 4.0cm from a diverging lens of focal length 6.0cm. Using both ray tracing and the thin lens formula, find the location and orientation of the image.
Homework Equations
-1/f = 1/so + 1/si
m = -si/so = hi/ho
The Attempt at a Solution...
θHomework Statement
The sun of (diameter D) subtends an angle of θ radians at the pole of the concave mirror of focal length f. The diameter of the image of the sun formed by mirror is _____
Homework Equations
1/v+1/u=1/f
The Attempt at a Solution
confused with question. Either i...
But if this is so, then in these photographs:
http://en.wikipedia.org/wiki/Bubble_chamber
http://en.wikipedia.org/wiki/Cloud_chamber
the "particle track - line of bubbles" shouldn't be able to be photographed so defined, but blureness should be photographed instead, since-if no lens was used...
The sun emits radiation in all directions. On the Earth, the rays from the sun are approximately parallel. Whatever side of the Earth is facing the sun at any given time is completely bathed in light.
When I look at the sun, I can see it as an object..ie. my eyes can figure out where the rays...
Homework Statement
A young lady wants to see herself in a small mirror, the ear to ear width of her face is 6 in and eye to eye is 4 in. What should be the minimum width of a mirror so that she can see her face completelyHomework EquationsThere a few equations which when directly applied give...
Homework Statement
Paralel light rays travel from air to a glass hemisphere with radius R and
index of refraction n_{g}that is greater than n_{air}. A top view is shown in the attached image.
(a) Where do the rays focus relative to the point P?
(b) The index of refraction of the...
Homework Statement
A 2.0--cm tall object is placed in front of a mirror. A 1.0--cm tall upright image is formed behind the mirror, 165 cm from the object.
What is the focal length of the mirror?
Homework Equations
The Attempt at a Solution
I tried 37 cm, it was incorrect
Homework Statement
An object is 12 cm in front of a concave mirror with a focal length of 21 cm .
Locate the image in s'
Is the image upright or inverted?
Homework Equations
willl get back with it
The Attempt at a Solution
Im not sure where to start, this should be a simple...
Homework Statement
The figure shows a meter stick lying on the bottom of a 100-cm-long tank with its zero mark against the left edge. You look into the tank at a 30^\circ angle, with your line of sight just grazing the upper left edge of the tank.
1)What mark do you see on the meter stick...
Simple Ray Optics Problem--Check my answer?
Homework Statement
You're helping with an experiment in which a vertical cylinder will rotate about its axis by a very small angle. You need to devise a way to measure this angle. You decide to use what is called an optical lever. You begin by...
Here's a question on ray optics.
We say that the focal length of a lens is half times the radius of curvature, right. Now, consider any lens(say convex), made of any material(say glass). Now a beam of light parallel to the principle axis, passes through the lens. All the rays in the beam will...
Hi,
I did a homework problem in which I was to show that a refracting telescope, modeled as a sequence of two thin lenses separated by a distance equal to the sum of their focal lengths, is capable of producing angular magnification. In my course we have been solving these questions in...
Here is the problem I am working on:
Sunlight enters a room at an angle of theta = 32° above the horizontal and reflects from a small mirror lying flat on the floor. The reflected light forms a spot on a wall that is d = 1.9 m behind the mirror, as shown in Figure 26-42. If you now place a...
Hello there,
I've been working on the following question:
A thin prism with a refraction index of n=1.41 has a top angle of 5.7 degrees. Find the angle of deflection for a light ray that falls on the prism surface : (a) normally
(b) At an angle of 4 degrees
I have worked out the second...