Optics: Total internal reflection problem

In summary, the problem involves finding the distance a man in a canoe paddles from a point directly above a lamp at the bottom of a 2m deep swimming pool. The lamp emits light in all directions and the critical angle of the light ray hitting the water surface is θc = 48.75. The solution requires finding the distance using similar triangles in a right triangle with the lamp as the vertex and the ray hitting the water surface at the critical angle.
  • #1
viny
1
0

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 sides of the pool do not reflect light.

n(water) = 1.33
n(air) = 1

Homework Equations


Total internal reflection: θc = sin-1 n(air)/n(water)

The Attempt at a Solution


I've found that the critical angle is θc = 48.75. However, I cannot seem to find the similar triangles required to find the distance.
 
Physics news on Phys.org
  • #2
You'll want a right triangle. The lamp is the vertex at the bottom and the hypotenuse is a ray from the lamp that hits the water surface at the critical angle (measured from the normal).
 

1. What is total internal reflection?

Total internal reflection occurs when a ray of light strikes the interface between two materials at a certain angle, called the critical angle. At this angle, the light is completely reflected back into the original material instead of passing through to the other material.

2. How is total internal reflection used in real-life applications?

Total internal reflection is used in various optical devices, such as prisms, optical fibers, and reflective coatings. It is also used in everyday objects, such as mirrors and windows, to reflect light and create images.

3. What factors affect the critical angle for total internal reflection?

The critical angle depends on the refractive indices of the two materials at the interface. It is also affected by the wavelength of light and the surface roughness of the materials.

4. Can total internal reflection be observed in other forms of waves besides light?

Yes, total internal reflection can occur with other forms of waves, such as sound and water waves. However, the conditions for total internal reflection may vary depending on the properties of the wave and the materials it is traveling through.

5. What happens to the light that is reflected during total internal reflection?

The light that is reflected during total internal reflection is reflected back into the original material. It does not pass through to the other material and is not absorbed by the interface. This allows for the formation of images and efficient transmission of light through optical devices.

Similar threads

Optics: refraction and reflection
    • Introductory Physics Homework Help
Replies
1
Views
937
What is the range of angles for total internal reflection in glass?
    • Introductory Physics Homework Help
Replies
12
Views
2K
Internal Reflection / Fiber Optics
    • Introductory Physics Homework Help
Replies
3
Views
2K
Total internal reflection: Question on angle of reflection.
    • Introductory Physics Homework Help
Replies
4
Views
1K
I Outer layer refractive index - total internal refection on waveguide
    • Optics
Replies
2
Views
1K
Find angle required for total internal reflection of a beam of light
    • Introductory Physics Homework Help
Replies
4
Views
6K
MC (multiple choice) question about total internal reflection
    • Introductory Physics Homework Help
Replies
11
Views
2K
Total internal reflection inside a fiber optic cable
    • Introductory Physics Homework Help
Replies
4
Views
2K
Optics: Total Internal Reflection with Triangular Prisms
    • Introductory Physics Homework Help
Replies
5
Views
5K
What is the Maximum Angle for Total Internal Reflection in a 30-60-90 Prism?
    • Introductory Physics Homework Help
Replies
9
Views
4K

Hot Threads

Recent Insights

Back
Top