What is Refractive index: Definition and 280 Discussions

In optics, the refractive index (also known as refraction index or index of refraction) of a material is a dimensionless number that describes how fast light travels through the material. It is defined as




{\displaystyle n={\frac {c}{v}},}
where c is the speed of light in vacuum and v is the phase velocity of light in the medium. For example, the refractive index of water is 1.333, meaning that light travels 1.333 times slower in water than in a vacuum. Increasing the refractive index corresponds to decreasing the speed of light in the material.

The refractive index determines how much the path of light is bent, or refracted, when entering a material. This is described by Snell's law of refraction, n1 sinθ1 = n2 sinθ2,
where θ1 and θ2 are the angles of incidence and refraction, respectively, of a ray crossing the interface between two media with refractive indices n1 and n2. The refractive indices also determine the amount of light that is reflected when reaching the interface, as well as the critical angle for total internal reflection, their intensity (Fresnel's equations) and Brewster's angle.The refractive index can be seen as the factor by which the speed and the wavelength of the radiation are reduced with respect to their vacuum values: the speed of light in a medium is v = c/n, and similarly the wavelength in that medium is λ = λ0/n, where λ0 is the wavelength of that light in vacuum. This implies that vacuum has a refractive index of 1, and that the frequency (f = v/λ) of the wave is not affected by the refractive index. As a result, the perceived color of the refracted light to a human eye which depends on the frequency is not affected by the refraction or the refractive index of the medium.
The refractive index varies with wavelength, this causes white light to split into constituent colors when refracted. This is called dispersion. It can be observed in prisms and rainbows, and as chromatic aberration in lenses. Light propagation in absorbing materials can be described using a complex-valued refractive index. The imaginary part then handles the attenuation, while the real part accounts for refraction. For most materials the refractive index changes with wavelength by several percent across the visible spectrum. Nevertheless, refractive indices for materials are commonly reported using a single value for n, typically measured at 633 nm.
The concept of refractive index applies within the full electromagnetic spectrum, from X-rays to radio waves. It can also be applied to wave phenomena such as sound. In this case, the speed of sound is used instead of that of light, and a reference medium other than vacuum must be chosen.In terms of eye glasses, a lens with a high refractive index will be lighter and will have thinner edges than its conventional "low" index counterpart. Such lenses are generally more expensive to manufacture than conventional ones.

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  1. C

    I Colloid complex refractive index from UV-vis spec

    Hi everyone, I am wondering, can I use the damped wave approximation for light travelling through a medium along with Beers law to spectroscopically determine a colloid complex refractive index. Thanks! Absorbance = exp (- 2πkx/λ) = ecl
  2. R

    B Radio waves -- Tissue Refractive Index

    The refractive index of tissue is approx. 1.4 for light, but with with lower frequencies the refractive index decreases. What is the tissue refractive index for radio waves 1 Hz - 1 MHz?
  3. Rymazon

    I Outer layer refractive index - total internal refection on waveguide

    I am interested in experimenting with AR lenses and one of the main technologies is a waveguide. They rely on total internal reflection, which needs light to go from a higher to lower refractive index medium. I am reading that current AR lenses use an outer layer with a lower refractive index to...
  4. orangephysik

    Glass prism and its refractive index

    Hi, I've attached the photo of the diagram, a photo of my drawings on the diagram. for a): Since the prism is an equalateral triangle, all angles inside the prism is 60°. This means the angle adjacent to α is 180° - 60° = 120°, which means the last angle is 180° - 24.5° - 120° = 35.5°. The...
  5. .Scott

    I Why is Cherenkov radiation blue? And what about refractive index?

    I got this question from my son last night. If you Google "Why is Cherenkov radiation blue", you get this: Somewhat more substantial is the Wiki article on the Frank-Tamm formula. That formula ties the Cherenkov radiation wavelengths to the transmission characteristics at any specified...
  6. bbbl67

    I Do materials have a refractive index for radio waves?

    It's been stated that the index of refraction of materials varies with frequency throughout the EM spectrum. What are the index of refraction for various materials in the radio frequency?
  7. N

    Lens Calculations using Refractive Index

    Answer: I already found the answer for Sin theta 2 like the pic below But, I am still not sure about how to derive delta here. Can anyone show me they way? thank you
  8. jaumzaum

    I Refractive index vs Temperature

    I was studying radio waves phenomenons and found this on Wikipedia: "Tropospheric ducting is a type of radio propagation that tends to happen during periods of stable, anticyclonic weather. In this propagation method, when the signal encounters a rise in temperature in the atmosphere instead of...
  9. T

    A Reflectivity with gradient in refractive index

    Hey all. Was wondering if anyone knew how I would go about determining the amount of reflectance that occurs when there is a gradual change in the refractive index. For example, if I have a material in air whose refractive index begins at e_r=1 (i.e. it matches the refractive index of the air)...
  10. mcas

    Estimate the following quantities from a graph of the refractive index of NaCl

    a) I managed to obtain some results that are roughly around what is given in the answers. Because \varepsilon_{st} and \varepsilon_{\infty} are values of \varepsilon_{1}, I used this approximation: n\approx \frac{1}{\sqrt{2}} (\varepsilon_{1}+\sqrt{\varepsilon_{1}^2})^{1/2} -> \varepsilon_{1} =...
  11. D

    Cauchy's law from Lorentz model

    Hello fellow physicists, I need to prove that when ##\omega << \omega_0##, Lorentz equation for refractive indexes: ##n^2(\omega) = 1 + \frac {\omega^2_p} {\omega^2_0 - \omega^2}## turns into Cauchy's empirical law: ##n(\lambda)=A+\frac B {\lambda^2}## I also need to express A and B as a...
  12. D

    Refractive index less than one

    Hello fellow users, I've been given the Lorentz model to calculate the refraction index of a dielectric, the formula in its simplest way states that: ##n^2(\omega) = 1 + \frac {\omega^2_p} {\omega^2_0 - \omega^2}## Where ##\omega_p## is the plasma frequency and ##\omega_0## is the resonance...
  13. Mayan Fung

    I Refractive index of a medium in relativistic motion

    I once naively think that the speed of light is also a constant in a medium in all inertial frames which is not the case. I tried to derive the result yet there is a discrepancy from the results I read in some articles. For example, from [Link to unpublished paper redacted by the Mentors], the...
  14. Mr_Allod

    EM Wave Reflection and Transmission Between 3 Materials

    Hello there. I set up the problem like this, I have a wave incident from air on the anti-reflective coating consisting of: ##\tilde {\vec E_I} (z,t) = \tilde E_{0_I} e^{i(k_1z- \omega t)} \hat x## ##\tilde {\vec B_I} (z,t) = \frac 1 v \tilde E_{0_I} e^{i(k_1z- \omega t)} \hat y## This wave gets...
  15. Another

    Kramers-Kronig relation for refractive index

    I don't understand why sometime for paper : Kramers-Kronig relations and sum rules of negative refractive index media for paper : A Differential Form of the Kramers-Kronig Relation for Determining a Lorentz-Type of Refractive Index* for paper : Comparison Among Several Numerical...
  16. A

    Which symbol is more relevant for refractive index: μ or n?

    both "mew"(sorry i couldn't get the symbol on on my keyboard so I'm writing it😊) and n are used for depicting refractive index i want to know which is more relevant and is there any reason for it or which symbol should be used in what cases.
  17. A

    Light speed and refractive index

    Refractive index of a medium is defined as : n = c / v; v is speed of light in medium. I believe n is never measured directly as here is no way to directly verify c / v. So what I guess is that all refractive index values are experimentally measured using n = sin α₁ / sin α₂. But then there is...
  18. I

    Different Temperatures of Ice versus the Refractive Index

    I want to make an experiment about the refractive index of ice but this time I want to use different temperatures. (for example with -15 C ice and with -1 C ice) When I tried to search on the internet I couldn't find any specific formula or any article because I guess I couldn't explain what I...
  19. E

    Path of light in material of continuously varying refractive index

    I've been playing around with this for quite some time now this morning but can't get the last bit out. I defined the time functional to be $$T[y] = \int_{x_1}^{x_2} \frac{\sqrt{1+(y')^{2}}}{c(y)} dx$$ which follows from consideration of the time taken to cover an infinitesimal section of arc. I...
  20. S

    Evanescent and Gradient force on an optical waveguide

    Let's say that on the surface of the cladding we have evanescent field due to the total internal reflection between the core and the cladding. The refractive indices of the the core is 1.45 and the refractive index of the cladding is 1.4, and I want to use the gradient force of the evanescent...
  21. VVS2000

    Refractive index of a prism using a spectrometer

    In the image attached, How is it that the angle shown is 2A? And what exactly is the position of min deviation? Why does it have to be in the given position as shown? Thanks in advance!
  22. Yaohui

    Other How to explain the relationship: refractive index vs permitivity?

    Any one can help deduct the process to obtain the following equation? n= squart(ε*μ), n=refractive index, ε=relative permitivity, μ=relative magnetic permitivity. I am reading a book relating to spectroscopy, and saw the above equation. I am really interested how the scientists got this...
  23. K

    Find the refractive index for the lens and find the image distance

    A thin lens has an upper radius of curvature 𝑅1 and a lower radius of curvature 𝑅2. When the lens is completely surrounded by air, it has a focal distance 𝑓. The lens is then placed in the interface between air and water inside a vessel (see figure). Calculate the refractive index for the glass...
  24. Manasan3010

    Refractive index using a traveling microscope

    For finding refractive index of a glass block, we use n=real-depth / apparent-depth For calculating apparent depth microscope is raised vertically until a clear focus is obtained of the underlying mark beneath the glass blob. Given that microscope is perpendicular to the mark, Wouldn't the...
  25. confusedhome

    I What is the refractive index of the Universe?

    I have not seen anything published siting a value, so being the curious type I was wondering if any has and what is the value? Also it would be nice to know at what Energy it is referenced to Thanks all, Bob
  26. S

    Refractive Index: Speed of Light in Medium vs Vacuum

    Dear Sir/Madam, Is the product of the refractive index of a medium and speed of light in the medium equal to the speed of light in vacuum? Thank You.
  27. kunalvanjare

    Refractive Index vs Conductivity

    Hello all, I would like to know which of the above two methods used in determining concentration of a solution is more accurate? Thanks, KV
  28. Penguin98

    How Is Destructive Interference Achieved in a Liquid Film on Glass?

    Mentor note: Thread moved from Adv. Physics Homework 1. Homework Statement Light is incident normally from air onto a liquid film that is on a glass plate. The liquid film is 174 nm thick, and the liquid has index of refraction 1.60. The glass has index of refraction n = 1.50. Calculate the...
  29. M

    The refractive index of an unknown liquid

    1. A light ray in dense flint glass that has an index of refraction of 1.655 is incident to the glass surface. An UNKNOWN liquid condenses on the glass's surface. Total internal reflection on the glass-liquid interface occurs for a minimum angle of incidence on the glass-liquid interface at...
  30. J

    How do I find the refractive index in sugar solutions?

    For class I conducted a experiment where I made sugar solutions, poured them into a glass prism container and used a laser pointer to find the refractive index. However, while typing in my results I realized I found the angle of deviation instead of the minimum angle of deviation since I didn't...
  31. S

    How do I find refractive index uncertainties?

    I've been doing an experiment where I've used prisms and a spectrometer to find the exact angles inside the prisms and the refractive index of the prisms by finding the minimum angle of deviation. I have attached a picture of the formula I've been using to find the refractive indices. Where...
  32. S

    Scattering from lossy medium whose refractive index is unity

    Consider a thin transparent plate surrounded by air. The plate's refractive index is exactly the same as the air's, but it does have a small loss (say of the order of 1%). Let the plate be vertical and normal to our "page" or your computer screen. A laser beam passes through the plate at an...
  33. AwesomeTrains

    Effective refractive index of a stratified medium

    Hello PF, I'm reading a paper for a project. In the paper they derive an equation for the effective refractive index ##n=\sqrt{\epsilon^{e} \mu^{e}}## of two stacked layers ##(n_1^2 = \epsilon_1 \mu_1, a)## and ##(n_2^2 = \epsilon_2 \mu_2, b)## where ##a,b## are the lengths and in my case...
  34. AwesomeTrains

    Trying to understand a derivation in a paper

    Hello PF, first of all I don't know where to put this post as it's not exactly a homework question but a clarification question for a project. I'm going through the derivation of the effective permeability of two stacked medias, given the polarization of an incoming EM wave but I'm stuck at the...
  35. T

    Deflection of wave in dissipative media with a complex refractive index

    Homework Statement A monochromatic plane wave with wavelength 500µm is propagating through a dissipative medium with refractive index 1-0.0002i. It approaching the edge of the medium, and will pass out into free space. If the angle of incidence is not 90°, how much will the wave deflect as it...
  36. spareine

    Why is the refractive index for red lower than for blue?

    By observing that red is the outermost color of the rainbow it is possible to conclude the refractive index of water, n, is lower for red than for blue. However, why is n lower for red? This seems to be answered by the Drude dispersion model, with a resonance in the ultraviolet region, but I...
  37. A

    Is there a limit to how steep the refractive index gradient can be

    Is there a limit to how steep a refractive index gradient can be before ray optics are no longer able to predict the path of the light? How is it related to wavelength? Under what conditions the light will be able to travel perpendicular to the gradient In a straight line? (having diffrent index...
  38. Bikash Kumar Das

    I Relative Permitivity, Permeability & Refractive Index of Water

    How does the relative permitivity and relative permeability related to the refractive index of a dielectic medium like water?
  39. T

    Refractive index of light from permittivity

    Homework Statement Given that the relative magnetic permeability and relative electric permeability of water are respectively, ##\mu_{rel}=1## and ##\epsilon=1.769## calculate the following 6 parameters. 1. Index of refraction of water ## n ## 2. speed of electromagnetic waves in water ## c...
  40. HappyBlue

    Mirror: refractive index and thickness

    Homework Statement Hello everyone ! I hope this is the correct place to ask. Here is my probem: I have to measure the refractive index and the thickness of the glass part of a mirror. The idea that I have, and that has been approved by my teachers, is the following: In order to measure the...
  41. Muhammad Danish

    Reflection and Refraction formula help

    Homework Statement 2. Homework Equations 3. The Attempt at a Solution [/B] I tried to solve this question with the general formula n=sin i / sin r. 1.5 = sin 30/sin r, r = 19.4 = 19 which is option A. But option A is incorrect. Please guide me where am I wrong..
  42. Ella98

    UV-Vis spectroscopy: Changes in refractive index

    I wanted to know how do you control for changes in refractive index when you get the UV-Vis spectrum of an aqueous solution in a double beam spectrometer? Is that something the equipment does automatically? Or something I have to do? Also, how do these changes in refractive index occur? Thanks...
  43. B

    Refractive Index of Coaxial Cable

    Anyone know the refractive index of a standard coaxial cable and have a traceable source?
  44. Richie Smash

    How to find unknown refractive index to solve for theta

    Homework Statement Hello, I will post a picture below. An optical device consists of two glass blocks of different indices of refraction, arranged as shown in the picture. The refractive index from air to medium 1 is 1.2, and the refractive index from medium 1 to medium 2 is 1.25 If light is...
  45. G

    I How energy of light is conserved when passing through medium

    The velocity of light changes when it passes through a medium of a different refractive index. So let's suppose the light is traveling through a vacuum at a velocity c and then passes through a glass wall. Its velocity decreases while traveling through it but then speeds back up to c after...
  46. Pushoam

    Refractive Index: Homework Answers

    Homework Statement Homework EquationsThe Attempt at a Solution I think that ## \frac { \sin \theta } {\sin \theta ' } = \frac { n_2} { n_1} ## I am taking the dielectric constant as 1 as the potential is 0 i.e. the medium is air.. So, ##n_1 = 1## For the 2nd medium, The dielectric...
  47. C

    Phase/group refractive index and reflection

    Let's consider a simlified ionosphere. It is a cold plasma without magnetic field and without electron-neutral collisions. The refractive index for radio waves is nf=sqrt(1-(w/wp)^2) (w is the frequency of the radiwave, wp the plasma frequency). It easy to demonstrate that the group refraction...
  48. V

    How would you calculate the refractive index?

    Homework Statement A plano-convex lens has a focal length f= 0.2 m. The radius of curvature of the convex side of the lens has been determined to be 0.07 m and the radius of curvature of the flat side is assumed to be infinite. Calculate the refractive index of the lens. Homework Equations 1/f...