Refraction through different mediums: calculating multiple angles help

In summary: Use Snell's law for all the boundaries. Don't need any 'basic laws of geometry'.I notice ##\theta_3 and \theta_4## are with respect to the plane rather than to the normal. This is not the way to go.I can't read your paperwork. Type your text. Use LaTex if you know it or want to learn it.
  • #1
lpettigrew
115
10
Homework Statement
Hello, I have a question concerning calculating the angles of refraction through different mediums. I have attached the questions and a photograph of my workings. I have answered the question fully and thoroughly shown my method but I would be extremely grateful if someone was able to review all of my workings to see if the angles I have calculated are correct. I have not faced such a broad refraction calculation problem like this before which is why I feel a little unsteady.
The question states ;
The image attached depicts three different mediums joined together. Block A has a refractive index of 1.52
Block B has a refractive index of 1.2
Block C has a refractive index of 1.4.
A ray of light travels through air into Block A, (assume air has a refractive index of 1.00).

1. The diagram displays the path of light when θ1 = 78.
Calculate all of the remaining angles up to and including the point where it leaves the blocks (θ2 to θ8).

2. Draw another diagram where the angle of incidence of θ1 = 68°. Calculate all of the angles up to and including the point where it leaves the blocks.
Relevant Equations
Snell's Law; n1sinθ1=n2sinθ2
1. I have calculated the first angle using Snell's Law and with subsequent proceeding angles I am uncertain whether my workings are correct since I have used basic laws of geometry that all internal angles of a triangle add up to 180 degrees and that alternate angles are equal to find proceeding angles in the same medium, e.g. to find θ3 I imagined a right-angled triangle, where θ2 and θ3 are the other interior angles.
θ3=180-(90+θ2)

I am not sure whether my methodology is correct or appropriate and would appreciate any advice on improvements I could make.

2. I have assumed the same method and proceeded to calculate angles θ2- θ8 accordingly. I must note that I realize the scale of my diagram is too small to properly exhibit the smaller angles (e.g. θ6=3 degrees) and I will draw another larger scale diagram as a better example.

Thank you to anyone who replies 😊👍
Workings to part 1.jpg
Workings to part 2.jpg
Question diagram.png
 
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  • #2
Just use Snell's law for all the boundaries. Don't need any 'basic laws of geometry'.
I notice ## \theta_3 and \theta_4 ## are with respect to the plane rather than to the normal. This is not the way to go.
I can't read your paperwork. Type your text. Use LaTex if you know it or want to learn it.
 
  • #3
rude man said:
I notice ## \theta_3 and \theta_4 ## are with respect to the plane rather than to the normal.
1592255244021.png


The blocks are arranged so that the indicated angles are all with respect to the normals.
 
  • #4
lpettigrew said:
I am not sure whether my methodology is correct or appropriate and would appreciate any advice on improvements I could make.
...
I must note that I realize the scale of my diagram is too small...

I think your method is correct.

You might see if you can relate ##\theta_8## directly to ##\theta_1## in one equation by combining the separate Snell's law equations before plugging in any numbers. You can then use this one equation to calculate ##\theta_8## for parts 1 and 2. Something interesting occurs regarding ##n_C##.
 
  • #5
TSny said:
I think your method is correct.

You might see if you can relate ##\theta_8## directly to ##\theta_1## in one equation by combining the separate Snell's law equations before plugging in any numbers. You can then use this one equation to calculate ##\theta_8## for parts 1 and 2. Something interesting occurs regarding ##n_C##.

The single equation relating ##\theta_8## directly to ##\theta_1## is applicable if there aren't any total internal reflections. So, I guess you still need to find the intermediate angles to identify any total internal reflections. My idea of a single formula might not be such a good idea after all. :blushing: Edit: Also, the question statement asks you to find all the angles! And, you need all the angles to trace the ray.

Check your work for part 2 at the A-B interface.
 
Last edited:
  • #6
TSny said:
I think your method is correct.

You might see if you can relate ##\theta_8## directly to ##\theta_1## in one equation by combining the separate Snell's law equations before plugging in any numbers. You can then use this one equation to calculate ##\theta_8## for parts 1 and 2. Something interesting occurs regarding ##n_C##.
Also if ##n_A =n_B## then the result is very interesting (and correct). I found it easiest to measure all the angles with respect to the vertical axis and use cosines in "Snell's Law" for the ##AB## interface. All you then need is ##cos^2+sin^2=1## The appropriate choice of square root takes care of any possible total internal reflection I think.
 
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  • #7
TSny said:
View attachment 264713

The blocks are arranged so that the indicated angles are all with respect to the normals.
Right you are.
 

Related to Refraction through different mediums: calculating multiple angles help

1. How does refraction occur when light passes through different mediums?

Refraction is the bending of light as it passes through a different medium, such as from air to water or from water to glass. This occurs because the speed of light changes when it travels through a different medium, causing it to change direction.

2. How do you calculate the angles of refraction when light passes through multiple mediums?

To calculate the angles of refraction, you will need to use Snell's Law, which states that the ratio of the sine of the angle of incidence to the sine of the angle of refraction is equal to the ratio of the speeds of light in the two mediums. This can be expressed as n1sinθ1 = n2sinθ2, where n1 and n2 are the refractive indices of the two mediums and θ1 and θ2 are the angles of incidence and refraction, respectively.

3. What is the refractive index and how does it affect the angles of refraction?

The refractive index is a measure of how much a medium can bend light. It is defined as the ratio of the speed of light in a vacuum to the speed of light in the medium. The higher the refractive index, the more the light will bend as it passes through the medium, resulting in a larger angle of refraction.

4. What are some real-life applications of refraction through different mediums?

Refraction through different mediums has many practical applications, such as in lenses for eyeglasses, cameras, and microscopes. It is also used in the design of optical fibers for telecommunications and in the production of prisms for splitting light into its component colors.

5. How does the angle of incidence affect the angle of refraction?

The angle of incidence is the angle at which light strikes the surface between two mediums. As the angle of incidence increases, the angle of refraction also increases, resulting in a larger amount of bending. This relationship is described by Snell's Law and is dependent on the refractive indices of the two mediums.

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