What is Snell's law: Definition and 141 Discussions
Snell's law (also known as Snell–Descartes law and the law of refraction) is a formula used to describe the relationship between the angles of incidence and refraction, when referring to light or other waves passing through a boundary between two different isotropic media, such as water, glass, or air.
In optics, the law is used in ray tracing to compute the angles of incidence or refraction, and in experimental optics to find the refractive index of a material. The law is also satisfied in metamaterials, which allow light to be bent "backward" at a negative angle of refraction with a negative refractive index.
Snell's law states that the ratio of the sines of the angles of incidence and refraction is equivalent to the ratio of phase velocities in the two media, or equivalent to the reciprocal of the ratio of the indices of refraction:
sin
θ
2
sin
θ
1
=
v
2
v
1
=
n
1
n
2
{\displaystyle {\frac {\sin \theta _{2}}{\sin \theta _{1}}}={\frac {v_{2}}{v_{1}}}={\frac {n_{1}}{n_{2}}}}
with each
θ
{\displaystyle \theta }
as the angle measured from the normal of the boundary,
v
{\displaystyle v}
as the velocity of light in the respective medium (SI units are meters per second, or m/s), and
n
{\displaystyle n}
as the refractive index (which is unitless) of the respective medium.
The law follows from Fermat's principle of least time, which in turn follows from the propagation of light as waves.
I am trying to figure out an intuitive understanding of how differential phase contrast (DPC) as a modality for measuring the phase shift as light passes through transparent samples. In a nutshell, DPC works by using either asymetric illumination or a split detector to standard compound...
Here, it's shown how white light, after passing from air to another medium, gets broken down into its constituent coloured rays. Each has its own refractive index in the medium, but it's only shown here red, blue and yellow. The auther comments on this image and says that, for small angles of...
Hello,
Something has made me confused after studying the Snell equations these days. Regarding the Balanis Advanced engineering electromagnetic( the pages have been attached), and based on that the reflection and transmission coefficient can be complex I need to rewrite the (5-23a) again...
My thoughts so far:
a. Since the critical angle occurs at the origin for the given parameters I would imagine that the maximum power reflected would be 100% since at the critical angle ##\theta_t = \frac \pi 2## and ##r_ {\perp} = r_{\parallel} = 1##. I do not know how I might go about finding...
From This picture, I think the fish will be smaller but the problem is how small will it be?
(Fish "L" is the image of fish "K")
Let ##H## be the depth of fish "K", ##\theta## be the angle of eyes to y-axis and ##n## is the index of refraction of water.
I was told to solve the second equation above for x to get l2 and l2, but that only gets me those in terms of other unknowns. I'm assuming I just need to solve t for my knowns, but I keep getting caught up by my unknowns. i.e., solving for x gives x = (l2*L*v2)/(l1*v1+l2*v2). Please note "l" is...
So far all I can work out is that the angle of incidence of the outer two and inner two rays is zero degrees, however, I can't work out how to get started on the problem. I feel like I need to use vertical slowness rather than the normal snell's law since I'm working with a dZ rather than a dX...
I for one don't see how ##\sin \theta_t \gt 1## is possible, even when you extend into the complex numbers. Is there even a way to order the complex numbers? Does he mean to say that the magnitude is greater than 1?
Anyway here's my attempt at interpreting what my instructor is trying to say...
Hi everyone,
Someone posted this hypothetical problem on a facebook group and I am wondering what your thoughts are.
The issue is that Snell's law does not seem to hold when applied to the transmitted wave (calculated using the electromagnetic interface conditions.) Here is an example...
Homework Statement
I have posted the snapshot of the problem.
Homework Equations
Snell's law equations
The Attempt at a Solution
Now the problem says that laser travels through air vertically upward to reach the outer surface of the glass half-cylinder. If that is the case, then from Snell's...
Considering classically a light ray in a medium with lightspeed ##c_1## and entering a medium with lightspeed ##c_2## moving with speed ##v## along let say ##y## in the plane of the interface, is it correct to obtain a very complicated formula, having even 3rd power of trigonometric functions of...
Homework Statement
Use Snell's law to show fresnel Eq 1 can be expressed as Eq 2
Eq 1 = (ncosθ-n'cosθ') / (ncosθ+n'cosθ)
Eq 2 = (tanθ' - tanθ) / (tanθ' + tanθ)
Homework Equations
nsinθ=n'sinθ' (Snell's law)
The Attempt at a Solution
n' = nsinθ / sinθ'
Substitute n' into equation and then...
I have been working a project of creating a simulation of thin-film interference in a 3D modeling program, Blender, to be able to create materials that would use its effects. While uncommon, I would love for it to be able to correctly calculate reflectance and transmittance when the incident...
With FIXED SOURCE AND RECEIVER, I have a light incident from fluid 1 with velocity v1 into fluid 2 with velocity v2. Obviously, according to Snell's law, v1/v2=sin(alpha1)/sin(alpha2), where alpha1 and alpha2 are the angles with regard to the vertical line.
My question is: how to calculate...
Homework Statement
A ray of light is traveling in a glass cube that is totally immersed in water. You find that if the ray is incident on the glass-water interface at an angle to the normal greater than 48.7°, no light is refracted into the water. Calculate the refractive index of the glass...
Homework Statement
https://gyazo.com/f8cf156e7bd2f2511e3fa859e3732fe6
Homework Equations
Snell's law.
The Attempt at a Solution
I'm mostly confused about the relevance of the second medium (of index n2) given that the distance between the ring and the boundary is "small". Having attempted to...
Homework Statement
Prove that snell's law ## {n_1}*{sin(\theta_1)} ={n_2}*{sin(\theta_2)} ## is derived from using euler-lagrange equations for the time functionals that describe the light's propagation, As described in the picture below.
Given data:
the light travels in two mediums , one is...
Hey guys,
is anyone here familiar with birefringence in uniaxial optical media?
In such a medium, there are only two types of polarizations allowed for a wave to propagate.
A wave with any other polarization will split into two waves with the allowed polarizations (ordinary + extraordinary wave...
When light from a rarer medium enters a denser medium, the wave gets refracted into the denser medium and so the wavelenght and the speed of propagation decreases ( [v][1] >[SUBv][/SUB2]) but the frequency remains the same. HOW ?
[SUBv][/SUB1] / [SUBλ][/SUB1] = [SUBv][/SUB2] / [SUBλ][/SUB2]...
Imagine I have a 10x10x10cm cube filled with a scintillating material (material capable of generating light when energized). Three cameras are looking at this cube from three orthogonal directions (x, y, and z). Light is generated inside the cube and is refracted as it leaves the cube and...
Well, I have checked out the ones with calculus but I was just wondering if there was one without calculus
I tried it but could not do it
I think Fermat's principle can be used to do it but I am not being successful
So, anyone please help
Hi all,
I'm after a little guidance for I do not know what is going wrong.
I understand that for Johann Bernoulli's proof of the brachistochrone problem he used refraction of light and Fermat's principle of least time.
I have decided to do a project on the subject, in which I am dividing up a...
Homework Statement
A 600 line/mm diffraction grating is in an empty aquarium tank. The index of refraction of the glass walls is [n][/glass] = 1.50. A helium-neon laser (lambda=633 nm) is outside the aquarium. The laser beam passes through the glass wall and illuminates the diffraction grating...
Homework Statement
Snell's law is:
$$\frac{\sin\theta_1}{c_1}=\frac{\sin\theta_2}{c_2}$$
$$\frac{c_1}{c_2}=n_{12}$$
Express ##\theta_2## as a function of ##\theta_1##
Find the largest value of ##\theta_1## for which the expression for ##\theta_2## that you just found is...
Homework Statement
Prove for effective index N that n1<N<n2.
Homework Equations
[/B]
N=n1sin(theta)
TIR is theta>thetacritical
snells law-n1sin(theta)=n2sin(theta2)The Attempt at a Solution
I know why N is strictly less than n1 since sin(theta) goes from 0 to 1 and if its at 1 theta has to...
I am learning principle of optics written by Born&Wolf and confused with the method to derive Snell's laws and law of reflection.
In the textbook,##v_1## is the speed of light in mediator 1 and ##v_2## is the one in mediator 2.
##{\vec s}## is the direction of light and ##{\vec r}## is the...
Homework Statement
I'm having trouble / uncertainties about the third missing angle (from left to right) in the picture. The first angle of reflection was easy as it's just 34 degrees as well and I used snell's law rearranged to find the first angle of refraction as 13.36 degrees from the...
Hi!
I'm doing a light research project and to have a refraction and reflection ( I don't know if it's like this in eglish) visual representation I came up with this photo. I don't know the name of this tool and also what is it made of? In my opinion is just a glass but I don't really know. Thanks!
Is the relativistic Snell's law : $$\frac {sin\theta_1}{sin\theta_2}=\frac {c_2}{c_1}\sqrt {\frac {c^2-c_2^2}{c^2-c_1^2}} $$ ? OR where could I check this ?
Homework Statement [/B]I am supposed to fill out a table with the values of θi and θr with the given information of n1 being 1.00 and n2 being 1.50 for the first row, and I am not quite sure how to do that just knowing the values that were given. I am also supposed to find the sine of θi and...
Homework Statement
A ray of light is incident on a flat surface of a block of gallium phosphide that is surrounded by water. The angle of refraction is 8.0°. Find the angle of reflection.
Homework Equations
n1 sin(theta1) = n2 sin(theta2)
The Attempt at a Solution
I keep finding different...
Homework Statement
Dispersion in a window pane. In Figure (a) below , a beam of white light is incident at angle θ1 = 67o on a common window pane (shown in cross section). For the pane's type of glass, the index of refraction for visible light ranges from 1.535 at the blue end of the spectrum...
At the start of the chapter the book told me to use this formula to find refractive index: N= Sin(i)/Sin(r)
How ever later in the section they showed me to use this formula when three quantities are given : NxSin(i)=NxSin(r)
I tried apply the same method to a question, it gave me a wrong...
I have a conundrum of sorts that has made me feel like an idiot and I am hoping someone can point out my mistake.
Suppose a light source is placed to the left of a prism and a detector is placed on the opposite side. I have seen plenty of pictures of this sort, and they all appear to show the...
I have light incident from plane with velocity v0 into plane with velocity v1. Obviously, according to Snell's law, v0/v1=sin(theta0)/sin(theta1), where theta0 and theta1 are the angles with regard to the vertical line. How to calculate d(theta0)/d(theta1)? There are probably arguments from...
Hi, I have a plane-wave incident upon a planar interface that is perpendicularly polarized with an electric field directed out of the page in the y-hat direction, perpendicular to the x-z plane of incidence. An image of the incident plane:
I'm also given the general expressions for the...
Homework Statement
[/B]
A student wants to find the refractive index of a rectangular block of glass. He draws around the block and marks the position of a ray of light that travels through the block. With the block removed, the student can draw in a normal line and then measure the angle of...
I can't figure out why my demonstration of snell's law fails, that's the demonstration: (I used a photo)
I think it fails because the function t (HO) represents a line and so the concept of minimum is not defined, when I take the derivative and equal it to 0 I'm considering the case when the...
If the the angle of incidence of an incident ray is less than (or equal to) the Critical Angle, the ray is refracted, but do we still get some reflection from this same incident ray?
Homework Statement
We look at the center of one face of a solid cube of glass on a line of sight making 55° with the normal to the cube face. What is the minimum refractive index of glass for which you will see through the opposite face of the cube? (Hint: see through will be possible if the...
Homework Statement
Suppose the isosceles prism of the figure(http://imgur.com/EQiQSoO) has apex angle φ = 53.4° and index of refraction n = 1.41. (a) What is the smallest angle of incidence θ for which a ray can enter the left face of the prism and exit the right face? (b) What angle of...
Hello!
This post is strictly related to my previous one. Let's consider the same context and the same image. Regarding the oblique incidence of a wave upon an interface between two dielectric, all the texts and all the lectures write an equation like the following:
e^{-j k_1 y \sin \theta_i} +...
Consider an interface along x-axis which separates two media. The medium below y = 0 is air or vacuum and light is incident from this medium onto the surface. The refractive index of the medium above y = 0 varies with x as some function of x : μ = f(x). Does the Snell's law still hold good ??
If...
Homework Statement
Calculating the refraction of index (n) with given information.
Homework Equations
The Attempt at a Solution
I tried to use Snell's Law but I have no idea about how I'm supposed to use it without angles. Instead, question gives distances. Need help very badly.