Question regarding optics(prism)

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In summary, to determine the index of refraction, n, in terms of θ for a 90 degrees triangular prism, the Snell's law of refraction is used. By using properties of angles and triangles, the equations sinθ = n sinθ1 and n sinθ4 = 1 can be obtained. By finding a relation between θ1 and θ4, it can be concluded that cosθ1 = 1/n, which leads to n in terms of θ.
  • #1
shakeysg
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Homework Statement



figure shows a 90 degrees triangular prism of refractive index n whereby light enters at point A with an incident angle of θ. The light then refracts at point B with an angle of refraction of 90 degrees.

determine index of refraction, n in terms of θ. refer to figure attached.


Homework Equations



using snell's law of refraction,

n.sinθ=n1.sinθ1

The Attempt at a Solution



first I used an snell's law to get an eqn

1.sinθ=n.sinθ1----------------------(1)

using properties of angles and triangles I got
θ2, θ3 and θ4.
θ1=θ3, θ2=θ4.

using snell's law again I got
n.sinθ4=1.sin 90 degrees
n.sinθ4=1

I tried using trigonometry to compute the thetas together and eventually eliminate θ1. But I was not able to do so. Am I missing something?
Since I got stuck, I thought if θ1=45 degrees, getting n in terms of θ is not a problem. But I reasoned to myself that it cannot be possible as I do not know θ4 and n. So making an assumption is not right. I think? I could be wrong though.. hmm..

help would be greatly appreciated and I am sorry if posted anything wrongly such as the format or thought process since this is the first time I am posting.

Thanks!

Syeh
 

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  • #2
You have two equations

sinθ = n sinθ1
n sinθ4 = 1

Can you find a relation between θ1 and θ4?
 
  • #3
hmm.. thanks for replying.. I went through that before.. basically 1=ncosθ1 since 90 degrees-θ4=θ1=θ3. and if i were to combine both eqns together, it will result in

sinθ=tanθ1.

the thing is I couldn't eliminate θ1 but I eliminated n instead. I even tried substituting other values of relevant θ into the equation and it got me more irritated. It feels like I am missing something right before my eyes and I cannot comprehend what is it that I missed. oh man. Anyway, this qns is the first part of a 4 parts 12 marks qns. So the solution shouldn't be too complicated. Thanks for replying again.
 
  • #4
shakeysg said:
basically 1=ncosθ1

So cosθ1=1/n. What is sinθ1 in terms of n?

ehild
 
  • #5
oh my. hahaa. thanks for making me rethink the qns. i managed to n in terms of theta. thanks again! : D
 

Related to Question regarding optics(prism)

1. What is a prism?

A prism is a transparent optical element with flat, polished surfaces that refract light. It is typically made of glass or plastic and is shaped like a triangular prism.

2. How does a prism work?

A prism works by refracting, or bending, light as it passes through the different mediums of the prism. This causes the light to separate into its component colors, creating a rainbow effect.

3. What are the different types of prisms?

There are several types of prisms, including triangular prisms, rectangular prisms, and pentagonal prisms. Each type has a different shape and can produce different effects on light.

4. What is the primary use of prisms?

Prisms have many uses in optics, but their primary use is to disperse white light into its component colors, known as a spectrum. This is commonly seen in rainbow effects or in spectacles for correcting vision.

5. How are prisms used in scientific experiments?

Prisms are commonly used in scientific experiments to study the properties of light, such as refraction and dispersion. They are also used in instruments like spectrometers to analyze the properties of light emitted by different sources.

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