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:

















{\displaystyle {\frac {\sin \theta _{2}}{\sin \theta _{1}}}={\frac {v_{2}}{v_{1}}}={\frac {n_{1}}{n_{2}}}}
with each


{\displaystyle \theta }
as the angle measured from the normal of the boundary,


{\displaystyle v}
as the velocity of light in the respective medium (SI units are meters per second, or m/s), and


{\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.

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  1. L

    A How to compute phase gradient from Snell's law?

    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...
  2. Ahmed1029

    I How can I derive this relation from Snell's law?

    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...
  3. Ahmed1029

    I Reflection, refraction, and Snell's law

    Where do the laws of reflection, refraction, and Snell's law come from in geometric optics? Are they derivable from basic laws of physics?
  4. tomceka

    Geometrical optics: using Snell's law, find the depth of the pool

    α=30°; l=0.5 m; n1=1; n2=1.33 α+β=90°, so β=90°-30°=60°. Using Snell's law: sinβ/sinγ = n2/n1 sinγ≈0.651 γ≈41°. β=γ+θ (vertical angles) θ=60°-41°=19° tan(θ+β)=l/h h=l/tan(θ+γ) h=0.5/(tan(19+41))≈0.289 m
  5. baby_1

    Complex Reflection and Transmission Coefficient in oblique incidence

    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...
  6. Mr_Allod

    Reflection and Refraction in an Elliptical Imaging Mirror

    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...
  7. K

    Size of a fish under water

    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.
  8. P

    Solving for earthquake transit time via Snell's Law

    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...
  9. P

    Finding the height of a focus point via ray tracing @ Snell's Law

    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...
  10. P

    Incidence on a conductor at an angle greater than the critical angle

    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...
  11. N

    Is Snell's law incompatible with interface conditions? What went wrong?

    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...
  12. I

    Snell's law problem about a hemispherical glass ball

    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...
  13. The proof of Snell’s law using springs - 3blue1brown

    The proof of Snell’s law using springs - 3blue1brown

    The law of light bending in matter. Also an important law for the proof of brachistochrone problem.
  14. jk22

    Is classical Snell's law with a moving medium solvable?

    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...
  15. S

    Fresnel Equations and Snell's Law

    Homework Statement From the Fresnel equations and Snell’s Law, prove that, when θ = θB where tanθB = nt/ni, (θB is the Brewster angle); (a) Reflection coefficient = 0 , and (b) transmission coefficient = n/n’ Homework Equations reflection coefficient = (ntcosθi - nicosθt) / (ntcosθi + nicosθt)...
  16. S

    Fresnel equation and Snell's law

    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...
  17. Jett

    Understanding a Generalization of Snell's Law

    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...
  18. ytht100

    Infinitesimal, Snell's law, and ray tracing

    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...
  19. DylanXO

    Solve Snell's Law: Glass Cube Refractive Index = 1.77

    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...
  20. L

    Snell's law question with a twist....

    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...
  21. C

    Proving Snell's law using Euler-Lagrange equations

    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...
  22. SchroedingersLion

    Birefringence in in uniaxial optical media and Snell's law

    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...
  23. T

    Wave optics / Snell's law of refraction

    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]...
  24. G

    Experimental evidence that Snell's law is correct

    Where can I find direct experimental evidence that Snell's law is correct for at least three of the typical spectral colours (say RGB). Thank you.
  25. D

    Multiple reflections and transmissions of light inside a cube

    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...
  26. shihab-kol

    Simple proof of Snell's law without calculus

    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
  27. Z

    Using Snell's Law for Brachistochrone Project

    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...
  28. S

    Diffraction grating problem involving Snell's Law

    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...
  29. En Joy

    How to find the quickest path?

    How to find the quickest path?
  30. K

    Snell's law and inverse function

    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...
  31. Alvis

    Prove n1<N<n2 for effective index N....

    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...
  32. Z

    Snell's law and law of reflection derivation -- confusing

    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...
  33. S

    Applying Snell's Law Inside & Outside a Prism

    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...
  34. L

    B What is this tool named?

    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!
  35. jk22

    I Relativistic Snell's law

    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 ?
  36. Zoey

    (Snell's Law) How do I find θi and θr?

    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...
  37. C

    Find Angle of Reflection for Snell's Law Q w/ GaP Index

    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...
  38. O

    Angle Spread with Snell's Law

    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...
  39. G

    Refractive index, Snell's Law

    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...
  40. Roger Dodger

    Fermat's Principle, Snell's Law, and the Prism

    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...
  41. ytht100

    Infinitesimal and Snell's law

    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...
  42. B

    Snell's Law: Parallel Polarization Derivation

    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...
  43. B

    Snell's law experiment with glass block

    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...
  44. P

    Snell's law demonstration?

    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...
  45. Seismic101

    Does reflection accompany refraction in Snell's law?

    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?
  46. M

    How can I find the minimum index of refraction?

    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...
  47. J

    Refraction in Isosceles triangle [Uni Phys 2]

    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...
  48. E

    Wave reflection and refraction, relations between angles

    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} +...
  49. Vaibhav Sahu

    Snell's law for an interface with variable refractive index

    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...
  50. O

    Refraction and Snell's Law, A complex question

    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.