What is the Minimum Refractive Index for Total Internal Reflection?

In summary, The problem involves using Snell's Law to find the refractive index of a material, with given values for the angles of incidence and refraction. The correct incident angle is 60 degrees, not 30 degrees as initially thought, and the angle of incidence is always measured from the normal.
  • #1
jegues
1,097
3

Homework Statement



See figure attached for problem statement.

Homework Equations





The Attempt at a Solution



Using Snell's Law,

[tex]n_{1}sin(\theta_{1}) = n_{2}sin(\theta_{2})[/tex]

[tex] n_{1} = \frac{n_{2}sin(\theta_{2})}{sin(\theta_{1})}[/tex]

Where,

[tex]\theta_{1} = 30^{o}, \theta_{2} = 90^{o}[/tex]

It gives me, [tex]n_{1} = 2[/tex] but the answer is a minimum of 1.15.

What did I do wrong/misunderstand?
 

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  • #2
hi jegues! :smile:

it's not 30°, it's 60° :redface:
 
  • #3
tiny-tim said:
hi jegues! :smile:

it's not 30°, it's 60° :redface:

Yes I figured that much but I don't understand why.

I'm looking at the triangle and the angle at the bottom right should be 90-60 = 30, that's where the incident angle is isn't it?
 
  • #4
hi jegues! :smile:
jegues said:
… the angle at the bottom right should be 90-60 = 30, that's where the incident angle is isn't it?

nooo :redface: … the angles of incidence and refraction are always from the normal :wink:
 
  • #5
tiny-tim said:
hi jegues! :smile:


nooo :redface: … the angles of incidence and refraction are always from the normal :wink:

So a line perpendicular to the surface it's hitting, right?
 
  • #6
s'right! :biggrin:
 

Related to What is the Minimum Refractive Index for Total Internal Reflection?

1. What is total internal reflection?

Total internal reflection is a phenomenon that occurs when a light ray traveling through a denser medium reaches the boundary with a less dense medium at an angle greater than the critical angle. Instead of refracting into the less dense medium, the light ray is completely reflected back into the denser medium.

2. What causes total internal reflection?

Total internal reflection is caused by the difference in the refractive indices of two media. When light travels from a denser medium to a less dense medium, it slows down and bends away from the normal line. If the angle of incidence is greater than the critical angle, the light will be reflected back into the denser medium.

3. What is the critical angle?

The critical angle is the angle of incidence at which total internal reflection occurs. It is determined by the refractive indices of the two media and can be calculated using Snell's law.

4. What are some applications of total internal reflection?

Total internal reflection is used in various applications, including fiber optics, prism binoculars, and reflective coatings for mirrors. It is also used in diamond cutting to create the brilliance and sparkle of diamonds.

5. Can total internal reflection occur in all media?

No, total internal reflection can only occur when light travels from a denser medium to a less dense medium. It cannot occur when light travels from a less dense medium to a denser medium, as the angle of incidence will always be less than the critical angle.

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