# What is Index of refraction: Definition and 167 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

n
=

c
v

,

{\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. ### Converting Voltage into Pressure

I am measuring the index of refraction of air using a Michelson interferometer. This set up includes a gas chamber that is placed on of the paths of source laser after it passes through a beam splitter. The gas chamber is pumped to vacuum, and then air is allowed to slowly enter the gas...
2. ### Ideal index of refraction for single layer AR coating

See statement.
3. ### Suspended particles and the index of refraction

Do suspended sub-micron sized particles influence the index of refraction of a liquid?
4. ### Index of Refraction Uncertainty Problem

A is the angle of refraction (~60 degrees) and Dm is the angle of minimum deviation that was different for each of the spectral lines associated to one of the six wavelengths measured. The problem I'm having is when I use equations of propagation of error to find the uncertainty in these...
5. ### Index of refraction and wavelength

The problem is multiple choice. A) refraction b) diffraction c) reflection d) dispersion An explanation would also be greatly appreciated!
6. ### Physics question: index of refraction

Homework Statement [/B] In order for the refracted ray R to have the same direction in space as the incident ray I, shown above, which of the following conditions by itself would be sufficient? (A) n1=n2 (B) n1=n3 (C) n2=n3 (D) Plane surface P, is parallel to plane surface P2- (E) None of the...
7. ### Is the index of refraction constant for a given medium?

If we have a medium (say, glass) with an index of refraction, n=1.33, the speed of light in it will be c/1.33. However, blue light travels slower in glass than does red light. Since c is constant and the speed of light is changing, doesn't that mean that the index of refraction will vary based...
8. W

### Calculating Index of Refraction with Wavelength

Homework Statement A beam of white light goes from air into water at an incident angle of 75 deg. What is the critical angle that the violet (410 nm) parts of the light is refracted? Homework Equations n1sin(θ1)=n2sin(θ2) n=c/v c=λf The Attempt at a Solution So sure, I get that the answer is...
9. ### Dependence of index of refraction on frequency

ok so recently i was doing dispersion of light and all of sudden something that i always took for granted came across the fact that blue light refracts more than red light then i recalled snells law and realized that it had no terms with the quantity of frequency in it (n sin θ = c) then i...
10. ### How does an index of refraction affect the EM field?

Hello. Say I have some refraction index n in a homogeneous material. Say I also have equations for the EM field (E and B vectors). Is it true to say that all that changes is the wavelength \lambda \to \frac{\lambda_0}{n} and consequently the wave vector k \to k_0 n ? Is it enough to account...
11. ### I Plasma self-focusing index of refraction < 1?

Hi. After reading about self-focusing in plasmas I came across the relative index of refraction that a light wave experiences during the interaction with plasma. Namely n = \sqrt{1-\frac{{\omega_p}^2}{{\omega}^2}} where \omega_p is the plasma frequency and \omega is the light (for example laser)...
12. ### Coating Eyeglass Lenses(destructive interference)

Homework Statement Eyeglass lenses can be coated on the inner surfaces to reduce the reflection of stray light to the eye. If the lenses are medium flint glass of refractive index 1.62 and the coating is fluorite of refractive index 1.432, (a) what minimum thickness of film is needed on the...
13. ### Index of Refraction: Range of Values?

as far as i know, when plugged in, SLM 's change index of refraction to accommodate the phase changes happening to the input (light). Is there a range for the possible values of the index of refraction?
14. ### Determining the the index of refraction

Homework Statement I must determine the refractive index of the adhesive tape. Tools I can have is: laser, tape, carton, scissors etc. I don't know how to do it. Homework Equations n=c/v n=sin alfa/sin beta The Attempt at a Solution I tried a lot of configurations to observe something but...
15. ### When can internal reflection be used to find the index of refraction

Homework Statement I need to describe an experiment in which I would use internal reflection to determine the index of refraction of material Homework Equations Snell's law The Attempt at a Solution I understand the concept of internal reflection, such as the critical angle etc. I am just...
16. ### Index of refraction of the material

Homework Statement A laser is fired into a wet paper placed ontop of a glass plate of thickness ##d## and an angle of ##0## degrees. When the light hits the paper and goes through the plate it forms a circle of light of radius ##R##. What is the index of refraction of the glass plate? Homework...
17. ### Index of when refraction/optics question

The question A microscope is focused on a black dot. When a 1.20 cm -thick piece of plastic is placed over the dot, the microscope objective has to be raised 0.380 cm to bring the dot back into focus. What is the index of refraction of the plastic Relevant equations/ideas...
18. ### Negative index of refraction transmission

Hi guys, I read a lots of papers about this theme, but still I don't understand what is going on. I have slab of negative index of refraction material, inside the material the evanescence field is amplified. I want to calculate transmission of this slab for evanescence waves, so I used fresnel...
19. ### Temperature dependence of the index of refraction of air

The index of refraction for a gas depends on temperature, as well as pressure. What is an experiment that would determine the temperature dependence of the index of refraction of air?
20. ### Index of refraction for converging lens

Homework Statement A thin converging lens has radii of curvature of R1=9cm and R2=-11cm. Assume its focal points F1 and F2 are 5cm from the center of the lens. Determine its index of refraction. Homework Equations Len's Makers equation: 1/f = (n2 - n1 / n1) (1/R1 - 1/R2) The Attempt at a...
21. P

### Question about index of refraction

according to wikiedia i can express the index as n= √(εrμr) but i also know that the index of refraction depends of the wavelenght but i don't see any λ in the equation, so ... why?
22. ### 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...
23. ### Index of refraction from reflected light (polarised)

Homework Statement A beam of light is reflected from the surface of some unknown liquid, and the light is examined with a linear sheet polarizer. It is found that when the central axis of the polariser (that is, the perpendicular to the plane of the sheet) is tilted down from the vertical at an...
24. ### Birefringence deviation angle?

The best known effect of birefringence is the lateral displacement of the extraordinary image. Why is this effect rarely quantified? I couldn't find a table of materials specifying the deviation angle δ of the extraordinary ray (say, for an angle of incidence equal to zero). Birefringence seems...
25. ### Law of Refraction with changing index of refraction

Homework Statement A light ray enters the atmosphere of the Earth and descends vertically to the surface a distance h = 101.2-km below. The index of refraction where the light enters the atmosphere is n = 1.00 and it increases linearly with distance to a value of n= 1.000293 at the Earth's...
26. ### Index of Refraction Measurement Uncertainty

Hello All, I am having some issues with calculating the measurement uncertainty when there is a mismatch in the index of refraction between a fluid and an interface. If am using an unobtrusive measurement technique such as Laser Doppler Velocimetry, how would I be able to quantify the...
27. ### Dispersion and the dependences of refractive indexes

I'm revising for a uni exam with past exam papers, and have gotten stuck on the details of dispersion. The two exam questions prompting this are a) What is the physical reason why the index of refraction for blue light is bigger than that of red light? and b) Explain how dispersion makes a...
28. ### Speed of sound and light through different solutions

If you have the same liquid, water, but with different ions dissociated in it, changing it's colligative properties, does the index of refraction change? And/or does the speed of sound through it change?
29. ### Refraction of Light question assistance needed

As revision for my upcoming physics exam, I'm doing an old exam paper from a previous year of the course, for which the answers aren't published. However, I'm stuck on a basic angle of refraction question: "A light ray makes an angle of 35degrees to the surface of an oil layer. [A diagram is...
30. ### Light Refraction on the Surface of a Sphere

Hello All, Using Snell's Law, it is pretty obvious how to calculate the angle of refraction when both index of refractions are known. My question is how would I apply this to a 3 dimensional situation, such as light refraction in a sphere? Since there are two angles in relation to the normal...
31. ### Solving index of refraction for Total Internal Reflection

Homework Statement Homework Equations Snell's Law n1sin(theta_1)=n2sin(theta_2) Total Internal Refraction: sin(theta_c)=(n_2/n_1) lambda_n=lambda_n The Attempt at a Solution So I drew the triangle and this is what I got, and well here is just a picture so far of what I have. [/B] I've...
32. ### Refraction through an optical fiber

Homework Statement Given a "new type" of optical fiber (index of refraction n = 1.23), a laser beam is incident on the flat end of a straight fiber in air. Assume nair = 1.00. What is the maximum angle of incidence Ø1 if the beam is not to escape from the fiber? (See attached file for...
33. ### Refraction Index problem

Homework Statement Unpolarized light hits a flat glass surface, 37.5 degrees to the surface's normal. The reflected light's polarization is investigated with a polaroid. The relationship between the max and min value of intensity from the polaroid when it is rotated is 4.0. What is the index of...
34. ### Index of Refraction Through a Cylindrical Tube

Hello All, I would like to start learning how to ray trace but the tracing through a tube with a thickness of t has got me stumped. If I have an n1 (outside tube), n2 (Tube), and n3 (inside tube). n1≠n2≠n3. Knowing Θ1 (the angle of incidence in relation to the normal), I can calculate Θ2 from...
35. ### Index of Refraction in prism

Homework Statement A ray of light passes through a prism, making the minimum angle of deviation. The rays enter and emerge at 37degree from the normal to the surface. What is the index of refraction of the material, if the prism angle is 50degree?[/B] Homework Equations...
36. ### Finding uncertainty for index of refraction

Homework Statement In an experiment to find the index of refraction, n, of a block of glass, the angle of incidence, θi , and angle of refraction, θr , were measured a number of times as follows: θi 10◦ 20◦ 30◦ 40◦ 50◦ θr 7.0 ◦ 13.5 ◦ 20.0 ◦ 25.5 ◦ 31.0 ◦ calculate the index of refraction n...
37. ### Light intensity and index of refraction

Hi. Will the amplitude of Poynting's vector change if the electromagnetic wave goes from one medium to another? Shouldn't the amplitude remain constant due to conservation of energy? I.e. the photon-density and velocity will change, but their total intensity remains the same. I could always do...
38. ### Shouldn't the index of refraction change?

Shouldn't the index of refraction change due to the random Brownian motion. I watched a video recently that explained why light slowed down in different mediums and said that it was due to the fact that the light ray has to bounce off several particles before it leaves the medium its in.(Note...
39. ### Why no transparent materials with large refractive index?

I know that the refractive index is determined by a material's dielectric constant and magnetic permeability. It's also true that we can treat the refractive index as a complex function with the imaginary part giving you an absorption spectrum. You can then get the index of refraction from...
40. ### Classical index of refraction theory

Is there such a thing as a classical theory for the index of refraction? I.e. are there expressions for the index of refraction ##n## in terms of other parameters like charge density? If so, a reference would be much appreciated.
41. ### [College Physics II: Waves/Optics] Index of Refraction

Homework Statement A solid glass cube with edge length of 10.0 mm and index of refraction n=1.75 has a small, dark spot dead center of the cube. Find the minimum radius of black paper circles that could be pasted at the center of each cube face to prevent the center spot from being seen, no...
42. ### Angle of refraction through a prism

Homework Statement In a physics lab, light with a wavelength of 570nmtravels in air from a laser to a photocell in a time of 17.5ns . When a slab of glass with a thickness of 0.890m is placed in the light beam, with the beam incident along the normal to the parallel faces of the slab, it takes...
43. ### Index of Refraction Question

Homework Statement The index of refraction is given by n^2 = (N q / ε m) (1 / (ω0^2 - ω^2 + iγω)) Where N is the electron density, q is the charge of an electron, ε is the permittivity of free space, m is the mass of an electron, ω0 is the resonant frequency, ω is the incident frequency...
44. ### Modeling index of refraction of dilute gases

I'm interested in predicting the index of refraction of atmospheric air and several nonpolar gases at room temperature for pressures of 1 atm - 0 atm. I'm not really sure where to get started. I have found the relation n=\sqrt{1+\frac{3AP}{RT}} but I don't really get where it comes from. Well...
45. ### Index of refraction below one

Hi, there. I don't understand how the light travel in the medium which has the index of refaction below one from the following topic: http://en.wikipedia.org/wiki/Total_external_reflection “For X-rays, however, all materials have indices of refraction slightly below 1. ” I did some...
46. ### MHB Index Refraction Yell Light Sodium Lamp Liquid 1.92E8m/s

The Speed of yellow light( from a sodium lamp) in a certain liquid is measured to be 1.92E8 m/s. What is the index of refraction of this liquid for the light?
47. ### Index of refraction - gas density formula

Could anyone please write the derivation (or forward me to the source of derivation) of the formula related these two properties. http://www.mathpages.com/home/kmath187/kmath187.htm the first fomula in this article. thanks
48. ### Index of refraction Thin Films

Homework Statement The diagram shows light incident from above on a film of thickness d. Each of the three materials in the figure can be chosen to be air, with index of refraction n=1.00, water, with index n=1.33, or glass, with index n=1.50. Under which of the following conditions will the...
49. ### Determining index of refraction and wavelength of a visible spectrum?

Homework Statement You decide to become a forensic pathologist because you enjoy working with dead people-they don't talk back-more than with the living. In one murder investigation, you find an unknown liquid in the victim's stomach. To identify this liquid, you pour a known amount of it onto...
50. ### Variable index of refraction

Homework Statement A narrow beam of light passes through a slab obliquely and is then received by an eye. The index of refraction of the material in the slab fluctuates slowly with time. How will it appear to the eye? Homework Equations The Attempt at a Solution Let a point object be kept at...