Angle of Incidence with partial reflection and partial refraction

In summary, the problem involves a beam of light in air striking a piece of glass with a refractive index of 1.51. The angle of reflection is twice the angle of refraction, and using the trig identity sin(2x) = 2sinxcosx, the angle of incidence is found to be 20.49 degrees.
  • #1
skibum143
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Homework Statement


A beam of light in air strikes a piece of glass (n=1.51) and is partially reflected and partially refracted. Find the angle of incidence if the angle of reflection is twice the angle of refraction.


Homework Equations


n1sintheta1 = n2sintheta2


The Attempt at a Solution


The angle of reflection equals the angle of incidence, which is twice the angle of refraction.
Therefore, I set up the equation as:
1 * sin (2theta) = 1.51 * sin (theta)
But when I try to solve for theta I get that they cancel out (sin 2theta / sin theta) just equals 2? I think I'm doing the trig wrong but I don't know why?
 
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  • #2
Yeah you are doing the trig wrong. You cannot just take the 2 out of the sin function and cancel.

Use this trig identity: sin(2x) = 2 sin x cos x
 
  • #3
yep, I'm awful at trig so that isn't surprising. haha.

i'm still not getting it right though: if i use that identity, i get:

1 * 2 sin theta cos theta = 1.51 * sin theta

If I divide the left by sin theta, the sin theta cancels out (right?), leaving me:
2 cos theta = 1.51
which gives me a theta of 40.97 deg, which is wrong...

Not sure what I'm doing wrong now...
 
  • #4
You need to double that angle, they ask for the angle of incidence not the angle of refraction.
 
  • #5
right. I'm an idiot. thanks for your help!
 
  • #6
Yep no problem.
 

1. What is the Angle of Incidence?

The angle of incidence is the angle at which a wave or ray of light strikes the boundary between two different mediums.

2. How is the Angle of Incidence calculated?

The angle of incidence is calculated by measuring the angle between the incident ray and the normal line, which is an imaginary line perpendicular to the boundary between the two mediums.

3. What is partial reflection and partial refraction?

Partial reflection and partial refraction occur when a wave or ray of light hits a boundary between two mediums and is partially reflected and partially refracted, meaning it is both reflected and bent as it passes through the boundary.

4. What factors affect the Angle of Incidence with partial reflection and partial refraction?

The angle of incidence with partial reflection and partial refraction is affected by the refractive indices of the two mediums, as well as the angle of the incident ray and the wavelength of the light.

5. How is the Angle of Incidence with partial reflection and partial refraction used in real-life applications?

The Angle of Incidence with partial reflection and partial refraction is used in various fields, including optics, telecommunications, and meteorology. It is used to understand and manipulate the behavior of light as it passes through different mediums, allowing for the creation of lenses, mirrors, and other optical devices. It is also used in the study of atmospheric refraction and the communication of signals through fiber optic cables.

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