Problem with light-ray construction

  • Context: Undergrad 
  • Thread starter Thread starter psychics_xxx
  • Start date Start date
Click For Summary

Discussion Overview

The discussion revolves around the construction of light rays in relation to the formation of a rainbow, specifically addressing the angles involved in internal reflection and refraction. Participants are examining the assumptions made in a diagram and the implications of those assumptions on the calculations presented.

Discussion Character

  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant questions the assumption that point B is located on a specific horizontal line through point O, suggesting that this may not be necessary for the analysis.
  • Another participant proposes that if point B were positioned differently, the reference frame could be "rotated" to maintain the same image, although they acknowledge this may not make sense.
  • A participant points out that the interior rays are symmetrical to a different axis than the exterior rays, arguing that rotating the reference frame would not resolve this discrepancy.
  • Concerns are raised regarding the representation of internal reflection at point B, with a participant noting that angle β must be equal to or greater than the angle of internal reflection, questioning why the ray is shown reflected at A but not at C.
  • Another participant corrects the critical angle for internal reflection at the water-air interface, stating it is approximately 41°, not 30°, and discusses the implications for the ray's path in the diagram.

Areas of Agreement / Disagreement

Participants express differing views on the assumptions made in the diagram and the implications of those assumptions. There is no consensus on the correctness of the initial calculations or the validity of the proposed adjustments to the reference frame.

Contextual Notes

Limitations include the unclear positioning of point B and the assumptions regarding the angles of incidence and reflection, which may depend on the specific definitions used in the context of the problem.

psychics_xxx
Messages
3
Reaction score
0
Hey, this is my first post so I am looking forward to see your answers! The problem is rather simply, it's about origin of rainbow. As you can see in image below, my calculations implies that always alpha = 2*betha which is of course wrong. Can someone prove why that is? It's all included in my notes but if some things need claryfication, just let me know.

1000014019.webp
 
Science news on Phys.org
psychics_xxx said:
View attachment 362586
Why do you assume that B is on the dashed horizontal line through O?
 
A.T. said:
Why do you assume that B is on the dashed horizontal line through O?
Well, maybe I am wrong, but if point B was a little bit higher or lower, can't we just "rotate" our refference and the image would be the same?
Ps. Yeah it does not make sens but the equation: theta = 4 beta - 2 alpha is correct and gives right angle 42 for caustic
 
psychics_xxx said:
can't we just "rotate" our refference and the image would be the same?
In your image, the interior rays are symmetrical to a different axis than the exterior rays. Rotating the reference frame cannot fix that.
 
You are showing the ray internally reflected at B. That's fine. However, it means that angle β is equal or greater than the angle of internal reflection. So why do you show the ray reflected at A but not also at C where the internal angle of incidence is also β?

Drop Refraction.webp
Also note that, for the water-air interface, the critical angle for internal reflection is about 41° not 30° as implied in your diagram. This means that your drawing should show the ray exiting at A. The drawing on the right is to scale.
The incoming horizontal ray is tangent to the circle at point A which is at the 12 o'clock position.
The refracted ray is at 41° withe respect to the vertical radius and intersects the circle at point B.
This internal ray is reflected (at what angle?) and intersects the circle at point C.
What is the internal angle of incidence at C and how should you draw the ray past that point?
 

Similar threads

Undergrad Prism Spectrometer Objective: Optics Question
  • · Replies 9 ·
Replies
9
Views
3K
Undergrad Condenser lens retrofit for a lighting application
  • · Replies 24 ·
Replies
24
Views
3K
Graduate When should I analyze optical problems using ray tracing vs. wavefront analysis?
  • · Replies 12 ·
Replies
12
Views
1K
Undergrad Why is there a sharp spike of blue light in my spectrometer readings?
  • · Replies 9 ·
Replies
9
Views
2K
Undergrad An Imagined Diffraction Grating
  • · Replies 7 ·
Replies
7
Views
895
Undergrad Image appears outside of q -- Lens Maker's Equation confusion
  • · Replies 17 ·
Replies
17
Views
3K
Graduate Please Explain My Polarized Light Experiments
  • · Replies 12 ·
Replies
12
Views
3K
Undergrad How to couple light from a very small source into spectrometer?
  • · Replies 10 ·
Replies
10
Views
2K
Undergrad It's still not clear to me what's the limit of light propagation
  • · Replies 6 ·
Replies
6
Views
3K
Undergrad Fabry-Perot Interferometer mirrors
  • · Replies 7 ·
Replies
7
Views
5K