What is Total internal reflection: Definition and 88 Discussions

Total internal reflection (TIR) is the optical phenomenon when waves travelling in one medium strike at sufficiently oblique incident angle (called the critical angle) against the boundary with another medium of lower refractive index, instead of transmitting into the second ("external") medium at a refracted angle, the waves all get reflected back into the first ("internal") medium. An example would be the water surface (the boundary between water and air) in a fish tank, which when viewed obliquely from below often reflects the underwater scenery like a mirror with no loss of brightness (Fig.  1).
TIR not only occurs with electromagnetic waves such as light and microwaves, but also with other types of waves, including sound and water waves. In the case of a narrow train of waves, such as a laser beam (Fig. 2), the reflection tends to be described in terms of "rays" rather than waves; in a medium whose properties are independent of direction, such as air, water or glass, the "rays" are perpendicular to the associated wavefronts.

Refraction is generally accompanied by small amount of partial reflection. When waves are refracted from a medium of lower propagation speed (higher refractive index) to one of higher speed (e.g., from water to air), the angle of refraction (between the outgoing ray and the surface normal) is greater than the angle of incidence (between the incoming ray and the normal). As the angle of incidence approaches the critical angle, the angle of refraction approaches 90°, at which the refracted ray becomes parallel to the boundary surface. As the angle of incidence increases beyond the critical angle, the conditions of refraction can no longer be satisfied, so there is no refracted ray, and the partial reflection becomes total. For visible light, the critical angle is about 49° for incidence at the water-to-air boundary, and about 42° for incidence at the common glass-to-air boundary.
Details of the mechanism of TIR give rise to more subtle phenomena. While total reflection, by definition, involves no continuing flow of power across the interface between the two media, the external medium carries a so-called evanescent wave, which travels along the interface with an amplitude that falls off exponentially with distance from the interface. The "total" reflection is indeed total if the external medium is lossless (perfectly transparent), continuous, and of infinite extent, but can be conspicuously less than total if the evanescent wave is absorbed by a lossy external medium ("attenuated total reflectance"), or diverted by the outer boundary of the external medium or by objects embedded in that medium ("frustrated" TIR). Unlike partial reflection between transparent media, total internal reflection is accompanied by a non-trivial phase shift (not just zero or 180°) for each component of polarization (perpendicular or parallel to the plane of incidence), and the shifts vary with the angle of incidence. The explanation of this effect by Augustin-Jean Fresnel, in 1823, added to the evidence in favor of the wave theory of light.
The phase shifts are utilized by Fresnel's invention, the Fresnel rhomb, to modify polarization. The efficiency of the total internal reflection is exploited by optical fibers (used in telecommunications cables and in image-forming fiberscopes), and by reflective prisms, such as the image-erecting Porro/roof prisms for monoculars and binoculars.

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  1. D

    Fraction of light reflected inside a diamond

    So i do now that it is a case of total internal reflection, but i didn't get R=1 for ##\theta_i=40.5^°##. I used the Fresnel equations for both s and p-polarized light and for s I got ##r_s=\frac{n_i\cos\theta_i-n_t\cos\theta_t}{n_i\cos\theta_i+ n_t\cos\theta_t}=0.296## using ##n_i=2.42## and...
  2. 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...
  3. E

    Angle of incidence and total internal reflection

    the angle of incidence at A is 40°, then why did the answer key say "angle of incidence at A is just less than 90°". it is obvious that 40° is quite far from 90° right?
  4. A

    EM wave reflected or transmitted?

    As I learn in class, when EM wave goes from medium 1 to medium 2, there are 3 possibilities that can happen Totally transmitted (i.e when the angle of incident is 0 degree) Partially transmitted and reflected (i.e when the angle of incident is between 0 and critical angle) Total internal...
  5. mgkii

    Frustrated Total Internal Reflection

    I've been reading into - and watching videos on - FTIR as an explanation of Quantum Tunnelling. The articles and videos I've watched switch between classical and quantum systems so frequently its left me with a question I can't find an answer to - the texts that seem like they might answer it...
  6. C

    Is there refraction upon frustrated total internal reflection

    In frustrated total internal reflection, is there refraction corresponding to the refractive index difference between the first and third medium or does the light continue in straight line as it is usually depicted in graphic representations of the frustrated total internal reflection?
  7. T

    What's the amount of energy lost in Total Internal Reflection?

    In Total Internal Reflection, the beam can still lose some energy as it reflects off the boundary of the medium it is within. This isn't covered under the Fresnel equations. The energy loss is probably lost in the form of evanescent waves. I tried searching for the formulae describing the...
  8. P

    I TIR (total internal reflection) in terms of quantum world

    how total internal reflection of light takes place in terms of quantum world?
  9. 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...
  10. T

    How does Total Internal Reflection in a mm/sm fiber work?

    I know Snell's Law and I do understand that there are single and multimode fibers. A fiber carries light hence to total internal reflection. so far so good. But is it only a single mode fibre that works with total internal reflection? And if so, how does the multimode fibre carry light then?
  11. T

    Energy Loss During Total Internal Reflection

    When a laser beam reflects during total internal reflection, how much of its intensity is lost? I can't the use Fresnel equations as this is for total internal reflection.If you don't know the answer to the above question, what about the same question, but for mirrors instead? What are the...
  12. SunandaGoh

    Total Internal Reflection / Reflection. What's the answer

    Homework Statement Homework EquationsThe Attempt at a Solution https://scontent-kul1-1.xx.fbcdn.net/v/t35.0-12/15146781_1334186669946177_363846788_o.jpg?oh=b75be99f63eba2e70db5e0287581076b&oe=583538C2 The answer given by the book is " Reflection ". But why isn't it Total Internal Reflection ?
  13. Cocoleia

    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...
  14. R

    Can light escape the medium when total internal reflection occurs?

    So I just very recentlyearned about total internal reflection, which basically states that when the incident angle is large enough, the light will reflect back into the medium. I have a few questions: Say we have a set up with a tank of water and a laser pointer in it 1) does this mean that if...
  15. G

    Total internal reflection, refractive index, optical fibres

    How does the claddibg with lower refractive index reduce the light loss from the core? Thank you.
  16. J

    Total Internal Reflection explained with Quantum Mechanics

    Is there an easy explanation of total internal reflection of light using Quantum mechanics(or QED)?
  17. cainko

    MC (multiple choice) question about total internal reflection

    Homework Statement There is an optical fiber.A light ray enter it at i°.Total internal reflection occur at X. What are the necessary conditions for the light ray to travel along the core of the fiber? (I have canceled B and D already.) A.n1>n2 and angle i should be greater than a certain value...
  18. K

    Frustrated total internal reflection superluminal

    When light encounters a boundary between a dense medium (glass) and a less dense one (air), it may undergo total internal reflection. But if there is another glass a short distance away, some light will jump the forbidden region by a tunneling process and enter the second glass medium. This jump...
  19. M

    Equations for total internal reflection

    If a beam of light undergoes total internal reflection, are there any equations to determine the angle of reflection based on the angle of incidence? Snell's Law: ## n_1sinA = n_2sinB ## is to my knowledge only valid under medium-to-medium transmission (for B: [0, pi/2]), correct? If total...
  20. RaulTheUCSCSlug

    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...
  21. R

    Multiplayer Refraction, Incident Angle

    Homework Statement The figure below shows the path of a beam of light through several layers (n1 = 1.58, n2 = 1.42, n3 = 1.20 and n4 = 1.00) of different indices of refraction. https://loncapa2.physics.sc.edu/res/brookscole/serway/College_Physics_7ed/Chap22/graphics/serw2244.gif a) If θ1 =...
  22. L

    Fresnel's Equations: Reflections and Total Internal Reflection

    I am trying to understand the derivation behind the equations for the phase shift incurred when light hits an interface between two lossless dielectrics under total internal reflection (TIR) from what I gathered in S. O. Kasap's Optoelectronics and Photonics. On the final pair of pages...
  23. S

    Total internal reflection: Question on angle of reflection.

    Homework Statement Suppose light from is moving from water to air. The critical angle be θ i.e. for angle of incidence θ, the angle of refraction is 90°. Refractive index of water wrt air be μ. Suppose the angle of incidence (i) is increased by 1° to θ+1. What happens to the...
  24. I

    Why in Optics total internal reflection happens this way?

    why total internal reflection happens only when a beam of light travels from a medium with higher index of refraction to a medium with lower index of refraction and not the other way around (i.e from a medium with lower index of refraction to a medium with a higher one)?
  25. N

    What is the range of angles for total internal reflection in glass?

    [b]1. Light traveling in air strikes a glass surface with n = 1.48. For what range of angles will total internal reflection occur? [b]2. sinΘc = n2/n1 [b]3. I did this equation with air as n2 and glass as n1 and then got Θc=42.5°. After that I subtracted that from the normal (90°)...
  26. G

    Frustrated total internal reflection: Where does energy come from?

    Hi, When we have total internal reflection of light at the boundary of an optically dense to an optically thinner medium, one can show that the component of the Poynting vector perpendicular to the boundary is zero, i.e. there is no energy flow into the thinner medium. However, the electrical...
  27. U

    Total internal reflection for a long time

    Imagine a square prism made from some material with such an index of refraction and surrounded by a substance of such index of refraction so that light rays entering the prism and hitting one of the internal sides of the prism at an angle of incidence 45° experience total internal reflection...
  28. G

    What is the Maximum Angle for Total Internal Reflection in a 30-60-90 Prism?

    Homework Statement Red light is incident in air on a 30o - 60o - 90 o prism as shown. The incident beam is directed at an angle of φ1 = 37.6o with respect to the horizontal and enters the prism at a height h = 26 cm above the base. The beam leaves the prism to the air at a distance d =...
  29. ShayanJ

    Details of total internal reflection

    Consider snell's law n_1 \sin{\theta_1}=n_2 \sin{\theta_2} ( n_1 and n_2 are real). We know that if n_2<n_1 , there exists an incident angle called critical angle that gives a refraction angle of ninety degrees i.e. \sin{\theta_c}=\frac{n_2}{n_1} . But if the incident angle is greater...
  30. A

    Exploring Total Internal Reflection: Why Does Light Path Through a 2nd Medium?

    Hi And Need Help The main Question is what happens to light and cause go into next medium as total internal reflection happens for incident angles higher than critical angle ? so the main question is why the light path throughout the second medium? We know when light travels from a medium...
  31. M

    Find angle required for total internal reflection of a beam of light

    Homework Statement An optical fiber consists of a glass core (index of refraction n1) surrounded by a coating (index of refration n2<n1). Suppose a beam of light enters the fiber from air at an angle θ with the fiber axis as shown in attached. (a) Show that the greatest possible value of θ...
  32. M

    Photonics Question - Laser and Total Internal Reflection

    Hello, this is my first post to this site. I had this idea a few nights ago, and I've been trying to wrap my head around it. Before I go ordering supplies to run some tests, I thought it would be worthwhile to gain some insight from you guys. Anyways, as you probably know, total internal...
  33. A

    Total internal reflection inside a fiber optic cable

    Homework Statement A multi-mode fiber optic cable has a core diameter d = 115 mm, ncore = 1.42, and ncladding = 1.17. What is the largest possible angle θin relative to the surface normal that light can enter the fiber (i.e. pass from air into the fiber core) and experience total internal...
  34. E

    Optics: Total Internal Reflection with Triangular Prisms

    Homework Statement When the striking ray is held perpendicular to the prism, there are four general configurations possible (in the attachment below). Use the figure on the next page to determine analytically which of these four configurations will result in total internal reflection of the...
  35. H

    Difference between Frensel reflection and Total Internal Reflection

    What exactly is the difference between Frensel reflection and total internal reflection with regards to the efficiency of an LED? Do they both occur at the semiconductor/ air interface? I am a bit confused, thanks for the help.
  36. S

    Total Internal Reflection and snell's law

    When we talk about Snell's law, and total internal reflection in particular, we usually will draw diagrams as if light is coming off a point in a single, straight line (that bends at an interface, of course). My question is, though, how does this light behave when it's coming off an extended...
  37. Drakkith

    Does total internal reflection only occur with electromagnetic waves?

    Does total internal reflection happen with all types of waves, or just electromagnetic ones?
  38. A

    Total Internal Reflection a doubt?

    I was reading about a case of total internal reflection in mirrors and something got me curious... Is there anything such as 'weak refractions'?? In the diagram of the mirror I saw, as a ray of light from an object entered a mirror, it was reflected by the silver coating, and then by the...
  39. S

    Is it Total internal reflection, or something else?

    Is this process known as "total internal reflection"? Or is it called something else? What is the name of this process that causes the entire material to light up even though the light is applied only to one side? Take a look at the photos so you can see what I am asking about. Notice how...
  40. L

    Total Internal Reflection: Finding the angle?

    Homework Statement The figure below shows a ray of light entering one end of an optical fiber at an angle of incidence i = 51.0°. The index of refraction of the fiber is 2.05. Diagram link: http://www.webassign.net/walker/26-55.gif (a) Find the angle the ray makes with the normal when...
  41. P

    Total Internal Reflection

    Homework Statement Find the lowest angle of θ1 given the apex angle is 60°. Air (n=1) is on the outside and inside (n=1.5) ϕ is defined as 60 degrees. Homework Equations The Attempt at a Solution θc = sin-1(\frac{1.00}{1.50}) = 41.81° To my understanding, θ1 must...
  42. V

    Optics: Total internal reflection problem

    Homework Statement A lamp is placed in the center at the bottom of a 2m deep swimming pool. The lamp emits light in all directions. Starting from a point directly above the lamp, a man in a canoe paddles until he no longer can see the lamp. How far did he paddle the canoe? Assume that the...
  43. F

    Does Total Internal Reflection Always Have Equal Angles?

    If there is total internal reflection, does the angle of incidence always equal the angle of reflection? Thanks
  44. F

    Does Total Internal Reflection Occur for Light Passing from Air into Water?

    Does total internal reflection occur if the refraction of light is passing from air into water? Thanks
  45. jegues

    Total Internal Reflection Confusion

    Homework Statement See figure attached. Homework Equations The Attempt at a Solution Initially, \theta_{c} = 60^{o} n_{glass}sin\theta_{c} = n_{air} So, n_{glass} = \frac{n_{air}}{sin\theta_{c}} Now I would think that the incident angle from glass to air would be...
  46. jegues

    What is the Minimum Refractive Index for Total Internal Reflection?

    Homework Statement See figure attached for problem statement. Homework Equations The Attempt at a Solution Using Snell's Law, n_{1}sin(\theta_{1}) = n_{2}sin(\theta_{2}) n_{1} = \frac{n_{2}sin(\theta_{2})}{sin(\theta_{1})} Where, \theta_{1} = 30^{o}, \theta_{2} =...
  47. K

    Total internal reflection zero

    How is that in refraction of light energy is lost but not in case of total internal reflection? Is the loss in total internal reflection exactly zero?
  48. A

    Struggling with Total Internal Reflection? Need Help for Exam Prep?

    Homework Statement Hi I wonder if anyone can help. I am having difficulty drawing refracted and total internally reflected rays. I have an exam on Monday. Can anybody recommend good websites that can help? Slight panic. Thanks Homework Equations The Attempt at a Solution
  49. M

    Total Internal reflection is Glass Prism Question

    Question about Total Internal Reflection? My textbook says that for total internal reflection to occur 2 conditions need to be met. Light is traveling more slowly in the first medium than the second medium and no.2 is the angle of incidence must be large enough for no refraction to occur. My...
  50. M

    Total Internal Reflection in Glass prism Question?

    Question about Total Internal Reflection? My textbook says that for total internal reflection to occur 2 conditions need to be met. Light is traveling more slowly in the first medium than the second medium and no.2 is the angle of incidence must be large enough for no refraction to occur. My...