What is Critical angle: Definition and 56 Discussions

In fluid dynamics, angle of attack (AOA, α, or


{\displaystyle \alpha }
) is the angle between a reference line on a body (often the chord line of an airfoil) and the vector representing the relative motion between the body and the fluid through which it is moving. Angle of attack is the angle between the body's reference line and the oncoming flow. This article focuses on the most common application, the angle of attack of a wing or airfoil moving through air.
In aerodynamics, angle of attack specifies the angle between the chord line of the wing of a fixed-wing aircraft and the vector representing the relative motion between the aircraft and the atmosphere. Since a wing can have twist, a chord line of the whole wing may not be definable, so an alternate reference line is simply defined. Often, the chord line of the root of the wing is chosen as the reference line. Another choice is to use a horizontal line on the fuselage as the reference line (and also as the longitudinal axis). Some authors do not use an arbitrary chord line but use the zero lift axis where, by definition, zero angle of attack corresponds to zero coefficient of lift.
Some British authors have used the term angle of incidence instead of angle of attack. However, this can lead to confusion with the term riggers' angle of incidence meaning the angle between the chord of an airfoil and some fixed datum in the airplane.

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  1. Lotto

    Calculate a radius of a circle on a screen

    The picture is here. The radius should be ##R=2.94\,\mathrm {cm}##. In the original solution, it is solved by using a critical angle ϵm. The b is the maximum distance at which a beam can refract. I understand this solution and an image of it is here: But I wanted to calculate it by knowing...
  2. kshitij

    What is the best shape for a soccer goal post?

    disclaimer: this is a made up question, so I don't know if there's a valid solution possible here First let's talk about the square post, it is clear that the shot will go in only if the ball hits the side AB of the square shown below, so the probability of a shot going in is simply ##\frac 1...
  3. G

    Critical angle (symmetry of refraction) confusion

    Refraction has a symmetry; on going from glass to air light at the glass air surfaces refracts away from the normal. If you turn the light source around and make the former refracted beam the incident beam then its refracted angle will be the former incident angle. So at critical angle, do the...
  4. dykuma

    How Can I Accurately Determine the Critical Angle in an Unknown Material?

    First, I attempted to find the wavelength of the incident wave in the required terms: Next, I tried to find the wavelength inside of the material: And then lasted, I tried to find the critical angle: My issue is that 1) I don't know if what I did was correct. 2) I don't think what I did...
  5. Nubira20

    What is the lateral distance ?

    I calculated the first critical angle and found the incident angle here to be greater than it thus there no echoes because the beam didn't refract , but i asked a friend and he told me no and that he calculated a number .. any help ?
  6. 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...
  7. S

    Critical angle: find the depth of the fish looking up

    Homework Statement A fish floats in water with its eye at the centre of an opaque walled full tank of water of circular cross section. When the fish look upwards, it can see a fish-eye view of the surrounding scene i.e. it is able to view the hemisphere of the scene above the water surface, and...
  8. Alvis

    Not a homwork problem, Fresnel Equations

    Homework Statement I was just curious, I know you can derive the critical angle using Snell's law..but could you use it using the Fresnel Equations of reflection, both of them? Homework Equations |r|=1 internal reflection of light...
  9. W

    Calculating the Minimum Force for Box to Move at Constant Velocity

    Homework Statement A force F is applied to a box of mass M at an angle θ below the horizontal (see figure). The coefficient of static friction between the box and the floor is μs, and the coefficient of kinetic friction between the two surfaces is μk. a) What is the minimum value of F to get...
  10. Samurai44

    Calculating Critical Angle: Relative vs. Absolute Refractive Index

    Greetings, Do we use Absloute refractive index when finding crtical angle ? if it was two mediums ( not vacuum or air) how would i calculate the critical angle ? I mean i get confused when I find relative refractive index because sometimes i get sine inverse greater than 1 which give no...
  11. T

    Confusion about EM Transmission coefficient - critical angle

    Hi, The reflection coefficient (R) of an EM wave is, as far as I know, 1 if there is total reflection and -1 if there is total reflection AND the phase changes by 180º. However, we also know that the transmission coefficient is given by T = R + 1 (or by its own formula, which should give the...
  12. E

    Critical angle for a box to start moving on an incline

    Homework Statement A ramp with an angle given by ø (from the horizon) and a box of mass represented by "m" with a given µ=0.55 between the ramp and the box, find the minimum (critical) ø for which the box will begin to move down the ramp. Wether µ is kinetic or static is not given in the...
  13. S

    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...
  14. M

    Does light reflect if incident exactly at critical angle ?

    A lot of textbooks and exam boards claim that light incident at exactly the critical angle is transmitted along the media boundary (i.e. at right-angles to the normal), but this seems to violate the principle of reversibility in classical physics. How would a photon or ray traveling in the...
  15. S

    Maximum critical angle for total reflection?

    Homework Statement A beam of light is incident on the boundary between a piece of glass to air. The index of refraction of the piece of glass is 1.4. Find the critical angle. It is quite simple to figure out this problem. Sinpheta critical = n2/n1 (as long as n1 is greater than n2)...
  16. N

    What is the critical angle for light traveling through glass?

    Light takes "t1" seconds to travel a distance "x" cm in vacuum and same light takes "t2" seconds to travel "10x" cm in a medium.The critical angle for the corresponding medium is .. ??
  17. H

    Critical angle (torque) at which the block tips over

    Homework Statement I know this tipping a block question has been asked many times and I know how to find the critical angle at which a block tips over. I was just wondering how one would go about analyzing the torque of the system. We all know that anywhere from 0 to the critical angle...
  18. A

    Finding the Critical Angle for T.I.R.

    Homework Statement When light strikes an air-material interface from the air side, Brewster’s angle is 63°. What is the critical angle for total internal reflection for light striking the interface from the material side? Homework Equations tanθB=n2/n1 sinθc=n1/n2 (n2 is...
  19. E

    Determining energy delivered from critical angle

    Q. An ultrasound shock wave is incident on a kidney stone which is immersed in urine. Using the data below, calculate the critical angle at the urine-kidney stone interface, and thus estimate the energy that will be delivered to the spherical stone. Assume intensity is uniform across the stone...
  20. R

    Refraction: Reflection after passing the critical angle

    If the angle of incidence is greater than the critical angle then it is reflected back into same medium. Is this reflection normal reflection? (as in it obeys all the rules of reflection, like reflection in mirrors) Or is it a bit different?
  21. K

    Designing Refraction Lab to Prove Critical Angle Equation

    I am trying to design a refraction lab involving the critical angle and I have an idea but I'm not sure if it is good or, for lack of a better word, stupid. Here it is: Using a laser and a rectangular container filled with water, I will shine the laser at the container and rotate the angle at...
  22. L

    Critical Angle of Glass Lab: Is My Graph Wrong?

    Homework Statement I'm doing a lab, and I plotted a graph for the refractive index I got about 38.3 degrees and the material I'm working with is a glass block from reading two textbooks I came to the conclusion my graph might be wrong =/, because the critical angle for glass in air is...
  23. S

    For n1 = 2.15 and n2 = 1.26, what is the critical angle so that all of

    For n1 = 2.15 and n2 = 1.26, what is the critical angle so that all of the incident light, from medium 1 to medium 2 is reflected? Im using Sin ic = n1/n2 For Sin ic i get =1.706 But the reverse Sin of that comes up math error? HELP
  24. M

    What is the critical angle and area for light at a water and air interface?

    Homework Statement calculate the critical angle for light at a water (n=1.33) and air (n=1) interface. if a fish is 2m below the surface of the water , calculate the area at the surface through which the fish can viw the world above the water. Homework Equations none given The...
  25. P

    Critical Angle of an Inverted pendulum

    Hi everyone, I’m designing and building an inverted pendulum on a cart for a 3rd year undergrad engineering course. So far i have been going quite well, but i have come across a question and it has me completely stumped. Any help would be great Homework Statement The pendulum on a cart only...
  26. B

    What causes the decrease in lift after passing the critical angle of attack?

    Hi, I'm a little confused as to why the lift acting on a body would decrease after the critical angle of attack has been passed. I understand the increase in Drag but i can't help but think that the top of the body would still have less pressure and lift would increase. As i write this I'm...
  27. Borek

    Snell's law and the concept of critical angle

    This is first of questions, I may have more, hence the very general title of the thread. I know the basic optics involved, two most important things here are Snell's law and the concept of critical angle - no problems here, even if I am just skimming on the surface. Problems start when I am...
  28. S

    Critical angle of refraction

    Homework Statement A ray of light travels across a glass-to-liqued interface. If the indices of refraction for the liquid and glass are, respictevly 1.75 and 1.52, what is the critical angle at this interface? Homework Equations critical angle = inverse sin (n2/n1) The Attempt at a...
  29. S

    Snell's law, critical angle & refraction

    Homework Statement Given a three layer model ------------------------------------------------- v_1=1.5km/s ------------------------------------------------- v_2=1.3km/s ------------------------------------------------- v_3=2.0km/s Assume a ray goes through layer 1 and hits the interface...
  30. D

    Critical angle inside cable

    A fiber optic (n = 1.5) is submerged in water (n = 1.33). What is the critical angle for light to stay inside the cable? i am so confuzed. this is the final question of my paper and i am stuck on a couple questions before this so it is obvious i would get this. i just need a start please.
  31. B

    Is critical angle diagram realistic?

    as per diagrams in textbooks, if incidence angle = critical angle then the ray should travel straight until it reaches the surface of the denser medium and then go tangentially to the boundary something like the following...
  32. M

    Critical angle- two climbers in a roped party

    Homework Statement -Two climbers are climbing up the frosted hillside in a roped party. How much does the most inclination have to be for them not to slip? -Second climber starts to slip downwards because he was not careful. The first climber notices this at once and tries to restrain the...
  33. R

    Snell's law, critical angle, and angle of incidence

    Homework Statement A pair of students measure the refraction of light in passing from acetone into air for several angles. When the angle of incidence is 30, the angle of refraction is 42. b) What is the angle of incidence (in degrees) when the refracted angle is the critical angle? Homework...
  34. J

    Critical Angle Homework: Speed of Light in Material is 1.61x10^8 m/s

    Homework Statement the critical angle for a ray of light leaving an unknown material (surrounded by air) is 32.4'(degrees celcius). the speed of light in the material is: Homework Equations niSin(theda)c = nRSin(theda)R (i am not sure how to make theda symbols on the computer)...
  35. F

    Critical angle = brewster angle?

    Homework Statement when the critical angle=brewster angle, what is the refractive index, if incident n is air=1. arcsin(1/n)=arctan(n)=>n=1.272...? how is this? i tried differentiating both side and solving but i just get into a big mess, can anyone help me if i am missing something?
  36. Q

    Finding the Critical Angle of Glass in Water

    Homework Statement The critical angle for a special glass in air is 44 degrees. What is the critical angle if the glass is immersed in water? Homework Equations sin(critical angle) = 1/index of refraction index of refraction of air is 1.00 index of refraction of water is 1.333...
  37. X

    Snell's Law and critical angle

    Homework Statement The critical angle of a certain plastic in air is 37.3 degrees. Wats the critical angle of the same plastic if its immersed in water? Homework Equations n1sin( theta)= n2sin(theta) The Attempt at a Solution Nair= 1.00 1.00sin37.3/1.33 = sin(theta) sin(theta)=...
  38. S

    Help with critical angle calculation

    Homework Statement A penny sits at the bottom of a pool of water (n=1.33) at a depth of 3.0m. If the observer 1.8m tall stands 30cm away from the ledge, how close to the side can the penny be and still be visible to the observer. Suppose there is another penny 10 times farther away than the...
  39. D

    Critical angle/ last angle of refraction

    Homework Statement A piece of glass has the shape shown in the below diagram. The index of refraction of the glass is 1.45. Find the critical angle for the glass. Sketch the path of the light ray until it emerges from the side of the figure and find the last angle of refraction...
  40. S

    Finding speed of light through medium, when given critical angle of refraction

    Homework Statement The critical angle of refraction for calcite is 68.4 (degrees) when it forms a boundary with water. Use this information to determine the speed of light in calcite. Homework Equations n=c/v n= Index of refraction c= Speed of light in a vacuum v= Speed of light in...
  41. G

    Critical Angle Geometric Optics

    There is a still-water lake and air interface. Light travels from the water to the air so that the incident angle is also a critical angle, making it so that the light runs along the surface of the water. Considering that this ray is reversible (air to water), a fish looking up at the surface...
  42. A

    Critical Angle Prism: Find Theta with n=1.90

    Homework Statement A corner reflector is to be made from a triangular prism with index of refraction n = 1.90, as shown in the diagram below. What is the maximum angle, with respect to the normal to the front surface of the prism, (theta), such that total reflection will occur...
  43. A

    Incidence, Refraction, Critical Angle

    Homework Statement Travellers in hot places often think that they see water in the distance, when there is nothing but land there. This effect is called a mirage. The air near the ground is very hot, and light reflects off the top of this layer of hot air. The diagram below shows how you could...
  44. D

    Critical angle and refraction

    Homework Statement A cubic container contains air, water, glycerin, amd diamond. There are no spaces between, and all boundaries are parallel. For light to travel through all of the substances, what is the maximum angle of incidence of the light ray in the diamond? Homework Equations...
  45. L

    Finding Critical Angle: A Freshwater Pond Problem

    Homework Statement Hey, I’m a little bit confused on an optics question on how to find the critical angle when given the indices of refraction for two different mediums. The question deals with a laser beneath the surface of a freshwater pond. The indices of refraction are r=1.33 for the...
  46. W

    What is the Critical Angle for Light Passing Through a Contaminated Lake?

    Homework Statement A point source of light is located 3.56 m below the surface of a large lake of clear, but contaminated, water (Lake Ontario, where n = 1.28). Find the area of the largest circle on the lake's surface through which light coming from the source can emerge into the air...
  47. A

    Finding the Critical Angle: Diamond and Water

    Homework Statement The critical angle diamond (n=2.42) and water (n=1.33). Find the angle. Homework Equations The Attempt at a Solution I dun get how u find the angle with 2 n's. I need a solution.
  48. M

    Help with Physics: Critical Angle and Refraction Questions

    hi.i m kinda new at this but i really need help in physics.i m stuck so much.ok i have tried this question but i don't get it even though i have followed the steps that is shown in the book. A layer of olive oil (n=1.47) floats on water. What is the critical angle for a ray directed from the...
  49. M

    Friction and critical angle question.

    I need... a lot of help. I spent an hour on this and a whole page of paper to no avail or certainty. http://img88.imageshack.us/img88/8794/phuhelphd1.png Suppose there is a diagonal downward force from top right to bottom left on an object with weight w on a surface with coefficient of...