Two Prisms connected by a material of refractive index n

In summary, the question is asking for the refractive index of a material, denoted as n2, that will cause light of a certain wavelength to follow a certain path. The refractive index of the material is dependent on the wavelength of light, and the critical angle for total internal reflection will also vary with the wavelength. The necessary refractive index for the transition between total reflection and transmission at a wavelength of 300 nm can be calculated as n2=n1*sin(theta1).
  • #1
Potatochip911
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Homework Statement


The prisms have a refractive index ##n_1=1.3## at wavelength ##\lambda=300nm## and are connected by a material with refractive index ##n_2##. What is the refractive index ##n_2## so that light of wavelength ##>\lambda## follow path 2, and light at ##<\lambda## follow path 3?
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Homework Equations


##\sin\theta_c=\frac{n_2}{n_1}##
##n=\frac{c}{v}=\frac{c}{f\lambda}##

The Attempt at a Solution



I am very confused as to how the wavelength of light effects total internal reflection. I can solve for the frequency of the light by using ##n=\frac{c}{f\lambda}\Rightarrow f=\frac{c}{n\lambda}## but I'm not entirely sure this is useful. I also have that ##\sin\theta_c=\frac{n_2}{n_1}## which can be rewritten as ##\sin\theta_c=\frac{\lambda_1}{\lambda_2}## The critical angle is a constant in this case I think? it's 45 degrees since the light is always coming in parallel to the bottom of the prisms but I don't understand how varying ##\lambda## is going to change whether or not it exits the prisms.
 
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  • #2
The question only says that n1 is 1.3 at a particular wavelength: 300nm. Do you suppose it could be different at other wavelengths? How would it vary?
 
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  • #3
The refractive index depends on the wavelength, so the critical angle depends on it as well. Here, the transition between total reflection and transmission is supposed to be at a wavelength of 300 nm, so you can calculate the necessary refractive index at 300 nm to be directly at the transition.
 
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  • #4
So the correct refractive index then is ##n_1=\frac{n_2}{\sin\theta_1}##, edit: I mean ##n_2=n_1\sin\theta_1## sorry for all the mistakes I'm on my phone
 

Related to Two Prisms connected by a material of refractive index n

1. What is the purpose of connecting two prisms with a material of refractive index n?

The purpose of connecting two prisms with a material of refractive index n is to create a prism system that can manipulate light in a specific way. By adjusting the angle and location of the prisms, the material can alter the path of light passing through them, allowing for the creation of various optical effects.

2. How does the refractive index of the material affect the behavior of the light passing through the prism system?

The refractive index of the material determines how much the light will bend as it passes through the prism system. A higher refractive index means that the light will bend more, while a lower refractive index will result in less bending.

3. Can the refractive index of the material be changed?

Yes, the refractive index of the material can be changed by altering its composition or by adjusting its temperature. This can result in different optical effects and allow for more precise manipulation of light in the prism system.

4. What are some practical applications of a prism system with two connected prisms?

A prism system with two connected prisms has many practical applications, including in optical instruments and devices such as cameras and telescopes. It can also be used in scientific experiments and research to study the behavior of light and to create specific optical effects.

5. Are there any limitations to using a prism system with two connected prisms?

While a prism system with two connected prisms can be very useful, it does have some limitations. The size and shape of the prisms, as well as the properties of the connecting material, can affect the precision and accuracy of the system. Additionally, the system may be limited in the types of optical effects it can produce.

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