# What is Angle of refraction: Definition and 34 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:

sin

θ

2

sin

θ

1

=

v

2

v

1

=

n

1

n

2

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

θ

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

v

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

n

{\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. ### 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...
2. ### 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..
3. ### Finding the angle of refraction

Homework Statement The refractive index of diamond is 2.42. A ray of light passing from the inside of a diamond into air makes an angle of incidence of 20 degrees. Find the angle of refraction. Homework Equations n = refractive index aNd = 2.42 (my book said the speed of light in a vacuum and...
4. ### When the incidence angle is equal to the angle of refraction

Homework Statement When the incidence angle is equal to the angle of refraction? Homework Equations sina/sinb=n2/n1The Attempt at a Solution I think as a=b => sina=sinb => n1=n2. We should have the same environment? But is that refraction?
5. ### Find Angle of Refraction: Snell's Law Solution

Homework Statement I need to find how a ray of light will travel from the snail towards Andrews eye. I need to find the angle of incidence and angle of refraction. I know the index of refraction of both materials Air: 1 Water 1.33 Homework Equations Snells law 1.33 *sin(X) = sin(y) x is...
6. ### Finding angle of refraction given angle of incidence?

Can someone help me in solving this question ? my attemp is sin42/sin 90 to get the refractive index then n =sin i/sin r to get c and for b n=1/sinc
7. ### Angle of Refraction through a Prism

Hello everyone, I am trying to figure out how to explain an aspect of this question to my students, but cannot seem to recall the geometry that explains the textbook's approach. In the figure below, for part (b) of the question, we are using the angles of refraction at the left boundary to...
8. ### Investigate one factor that affects the angle of refraction

Statement: I need a suitable method and factor to investigate ONE factor that affects the angle of refraction. It has to be related to the context of everyday life and glasses, i.e. how glasses are used to focus light and the light focused is that of a refracted ray. Therefore factors such as...
9. ### 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...
10. ### Angle of Refraction Given Wavelength & Speed of Light in Air & Glass

Homework Statement Light of wavelength 600 nm in air enters a piece of glass. The speed of light in this glass is 0.650 times the speed in air. Calculate the angle of refraction, Given that the angle of incidence of this light ray is 40°. Homework Equations Snell's Law Sin(θ1)/sin(θ2)...
11. ### Angle of refraction, Refractive Indices, and D Vectors

Homework Statement At the He-Ne laser wavelength (L= 632.8 nm) the refractive indices of crystal quartz are n o = 1.54264 and n e = 1.55171 calculated from its Sellmeier equation. The laser is incident from the air onto the surface of crystal quartz at an angle of incidence of 45 degrees...
12. ### MHB Angle of refraction, Refractive Indices, and D Vectors

I have no idea how to do this or where to start. Can someone please help me? At the He-Ne laser wavelength (L= 632.8 nm) the refractive indices of crystal quartz are n o = 1.54264 and n e = 1.55171 calculated from its Sellmeier equation. The laser is incident from the air onto the surface of...
13. ### Snell's Law - complex angle of refraction (need complement )

Snell's Law - complex angle of refraction (need "complement") I'm tying myself in knots trying to calculate something I think should be very simple. I'm writing/debugging some code at the moment, and I simply don't know if this silly problem is the source of the major errors I'm currently...
14. ### Angle of refraction snells law

im having difficulty understanding how light leaves a prism mainly because I am not sure about what angles we are talking about when we say angle of refraction/incidence. Lets say for example light hits a triangular prism leg at a 90 degree angle (incidence = 90 deg?) and the prism has index of...
15. ### How do you find the difference in the angle of refraction?

Homework Statement Sunlight strikes a piece of crown glass at an angle of incidence of 36.7 degrees. Calculate the difference in the angle of refraction between a orange (610. nm) and a violet (410. nm) ray within the glass. The indices of refraction for the orange and the violet are n = 1.522...
16. ### Solve Angle of Refraction Problem: Incident 35°, Refracted 22° & Leaving 38°

Homework Statement Hi I have this little problem bothering. The question goes like this: A ray enters an equilateral glass prism of refractive index 1.55 at the midpoint of one side of the prism at an angle of inceidence of 35 degrees. a. Sketch this arrangement and show that the angle of...
17. ### 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...
18. ### Why Does the Angle of Refraction Change in Borosilicate Glass Experiments?

Hello; For my physics investigation I'm investigating a relationship between wavelength and index of refraction for a medium exhibiting normal dispersion. The medium is borosilicate glass (BK7). However, I'm encountering some problems that I didn't expect. For example, directing a red ray of...
19. ### Angle of refraction of light in water

Homework Statement A ray of pure yellow light reaches the surface of a pond at an angle of incidence of 60°. What angle does it make with the normal inside the water? Speed of light in air = 300,000,000 m/s Speed of light in water = 225,000,000 m/s So the Refractive index μ = 1.33...
20. ### Angle of incidence, angle of refraction and angle of reflection

Homework Statement A light ray strikes the surface between two transparent materials as shown. Each angle is labeled with a letter. Give the letters for the angle of incidence, angle of refraction and angle of reflection, in that order Homework Equations...
21. ### Angle of Refraction: Find Low Power Laser Incident Angle

Homework Statement A low power laser is incident at the interface between crown glass (n=1.52), and air at an angle of 45 degrees. The refracted ray into air makes an angle with respect to the normal of the surface that is closest to ... Question 2 answers 27.7 degrees 41.1 degrees...
22. ### Can the angle of refraction be equal to the angle of incidence?

Snell's law says n1sin(theta1) = n2sin(theta2) The angle of refraction theta2 can be greater or less than the angle of incidence theta1. That's fairly obvious. My question is if theta2 = theta1 then we don't have an interface (because n1 = n2) so the light is still in the same medium, and...
23. ### Physics3, angle of refraction, beam displacement

hi everyone, I've got another question. i feel good about my methods, but I'm getting an incorrect answer. Homework Statement A ray of light impinges at a 60° angle of incidence on a glass pane of thickness 6 mm and index of refraction 1.50. The light is reflected by a mirror that touches...
24. ### Angle of Refraction for Red & Blue Light

Homework Statement The index of refraction for a diamond for red light, 656 nm, is 2.410, while that for blue light, 434 nm, is 2.450. Suppose white light is incident on the diamond at 30.0 degrees. Find the angles of refraction for these two colors. Homework Equations n1sinangle of...
25. ### 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...
26. ### 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...
27. ### Trace the path of the light ray and find angle of refraction

Homework Statement A ray of light strikes the midpoint of one face of an equiangular (60◦, 60◦, 60◦) glass prism (n = 1.3) at an angle of incidence of 33◦. a.Trace the path of the light ray through the glass, and find the angle of refraction at the first surface. b.Find the angle of...
28. ### Angle of Refraction: 60 Degrees

Homework Statement If the sound wave hits the cold air interface at an angle of 60, what is the angle of refraction? The speed of sound as a function of temperature can be approximated by v = (331 + 0.60T) m/s, where T is in Celcius. Homework Equations The Attempt at a...
29. ### Angle of refraction through ice into water

Homework Statement A layer of ice having parallel sides floats on water. If light is incident on the upper surface of the ice at an angle of incidence of 15.0°, what is the angle of refraction in the water? Homework Equations The Attempt at a Solution i know its not so simple that...
30. ### Calculate the angle of refraction for a substance

Homework Statement Calculate the angle of refraction for a substance that has a critical angle of 50.5 degrees when that substance is in the air. Homework Equations Apparently the equation I need is: ni *• sine() = nr • sine () My problem is, I have no idea how to use this...
31. ### Finding Angle of Refraction with Given Angles

does anybody know formula for finding angle of refraction with given angles of incidence in the medium and the angle of refraction?
32. ### Calculate Red Light Wavelength in Liquid | Angle of Refraction

Red light travels from air into liquid at an angle of incidence of 390 and an angle of reflection of 170. Calculate the wavelength of the red light in the liquid if its wavelength in air is 750 nm can you give me some hint for this one too? :cry:
33. ### Angle of Refraction: Prove Incident Beam is Parallel to Emerging Beam

A light beam passes from medium 1 to medium 2 with the latter being a thick slab of material whose index of refraction is n2. Show that the emerging beam is parallel to incident beam. Am I correct in assuming that the only way this is possible is to have the incident beam making an angle that...
34. ### Measuring the Angle of Refraction in a Triangular Prism Lab

I did a lab in school where I took a triangular prism and shined light though it. I measured the angle of incidence and angle of refraction for three different angles. The lab question first told me to find the index of refraction of the prism using the two angles. That was easy. The next...