Snell's law, critical angle & refraction

In summary, we discussed the concept of critical angle in a three layer model, where a ray goes through layer 1 and hits the interface between layer 1 and layer 2. We used Snell's law to find the critical angle, which is equal to the ratio of refractive indices of the two layers, n2/n1. The velocity of light in the medium is represented by v, and the subscript for the refractive index changes because v1 is equivalent to c/n1 and v2 is equivalent to c/n2.
  • #1
sveioen
14
0

Homework Statement


Given a three layer model

-------------------------------------------------
[tex]v_1=1.5[/tex]km/s
-------------------------------------------------
[tex]v_2=1.3[/tex]km/s
-------------------------------------------------
[tex]v_3=2.0[/tex]km/s

Assume a ray goes through layer 1 and hits the interface between layer 1 and layer 2. What is the critical angle?

Homework Equations



Snells law
[tex]\frac{\sin \theta_1}{\sin \theta_2}=\frac{v_1}{v_2}[/tex]

The Attempt at a Solution



To find the critical angle, you normally take [tex]\sin \theta_c = \frac{v_1}{v_2}=\frac{1.5}{1.3}[/tex]. But in this case that means I have to take [tex]\sin^{-1}[/tex] of a value that is over 1! How do I solve this?
 
Physics news on Phys.org
  • #2
According to Snell's law
n1sin(θ1) = n2sin(θ2)

If θ1 is θc, then θ2 = 90 degrees.

So sin(θc) = n2/n1
 
  • #3
rl.bhat said:
According to Snell's law
n1sin(θ1) = n2sin(θ2)

If θ1 is θc, then θ2 = 90 degrees.

So sin(θc) = n2/n1

When I look up Snell's law on Wikipedia it says

[tex]
\frac{\sin \theta_1}{\sin \theta_2}=\frac{v_1}{v_2}=\frac{n_2}{n_1}
[/tex]

Why does the subscript change in the [tex]n_n[/tex] ? Isnt [tex]v_1=n_1[/tex] and [tex]v_2=n_2[/tex]?

Thanks for answering
 
  • #4
According to the definition,
refractive index n = c/v. where c is the velocity of light in vacuum and v is the velocity in the refracting medium.
So v = c/n
Or v1 = c/n1 and v2 = c/n2
then v1/v2 = ...?
 
  • #5


The critical angle is a special angle at which the incident angle causes the refracted ray to travel along the interface between two materials. In this case, the critical angle can be found using Snell's law, which relates the angles of incidence and refraction to the velocity of the wave in each material. However, as you have noticed, in this case the velocity of the wave in the first material is greater than the velocity in the second material, resulting in a value greater than 1 when calculating the sine of the angle of incidence. This means that there is no critical angle for this specific scenario.

In general, when the velocity in the first material is greater than the velocity in the second material, there is no critical angle and the incident ray will always be refracted into the second material. This is known as a non-total internal reflection scenario. However, if the velocity in the first material is less than the velocity in the second material, there will be a critical angle and the incident ray can be completely reflected back into the first material, known as total internal reflection.

In summary, for this specific three layer model, there is no critical angle at the interface between layer 1 and layer 2. This is due to the fact that the velocity in layer 1 is greater than the velocity in layer 2. To find the critical angle in other scenarios, you can use Snell's law and ensure that the velocity in the first material is less than the velocity in the second material.
 

What is Snell's law?

Snell's law, also known as the law of refraction, is a formula that describes the relationship between the angle of incidence and the angle of refraction when a light ray passes through a boundary between two different mediums, such as air and water.

What is the critical angle?

The critical angle is the angle of incidence at which the angle of refraction is 90 degrees. This occurs when light passes from a medium with a higher refractive index to a medium with a lower refractive index.

How does refraction work?

Refraction is the bending of light as it passes from one medium to another with a different density. This bending occurs because light travels at different speeds in different mediums, causing it to change direction when it enters a new medium.

What factors affect the angle of refraction?

The angle of refraction is affected by the difference in density or refractive index between the two mediums, as well as the angle of incidence. Additionally, the speed of light in each medium also plays a role in determining the angle of refraction.

What are some real-life applications of Snell's law and refraction?

Snell's law and refraction have many practical applications, including the design of lenses and prisms used in optics, the correction of vision in eyeglasses and contact lenses, and the phenomenon of mirages. They also play a crucial role in the field of fiber optics, which is used in telecommunications and medical imaging.

Similar threads

  • Introductory Physics Homework Help
Replies
7
Views
1K
  • Introductory Physics Homework Help
Replies
3
Views
768
  • Introductory Physics Homework Help
Replies
6
Views
948
  • Introductory Physics Homework Help
Replies
1
Views
863
  • Introductory Physics Homework Help
Replies
15
Views
5K
  • Introductory Physics Homework Help
Replies
4
Views
2K
  • Introductory Physics Homework Help
Replies
8
Views
4K
  • Introductory Physics Homework Help
Replies
2
Views
1K
Replies
6
Views
1K
  • Introductory Physics Homework Help
Replies
1
Views
2K
Back
Top