Geometric Optics- Refraction , reflected ray's

In summary, the student was trying to solve a problem involving the angles of incidence, reflection, and refraction. They were not sure where to start and were confused. They eventually figured out the angle of refraction and critical angle, but were still confused about the index of refraction.
  • #1
sally143
5
0

Homework Statement



A beam of light in air makes an incident angle with the normal at 53 with an unknown substance. Part of the light is relected and part is refracted into the substance. The reflected ray and the refracted ray make an angle of 90 degrees.

a) What is the refracted angle?
b) what is the index of refraction for the substance?
c) the critical angle if the ray goes from the unknown substance into air?


Homework Equations


I think we use , Snells law nsin() = nsing () ; where () = Angle



The Attempt at a Solution

 
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  • #2
Welcome to PF!

Hi sally143! Welcome to PF! :wink:

Yes, that's ok so far …

now show us how far you get, and then we'll know how to help! :smile:
 
  • #3


tiny-tim said:
Hi sally143! Welcome to PF! :wink:

Yes, that's ok so far …

now show us how far you get, and then we'll know how to help! :smile:

Im confused, and not sure. But Incident angle is =53 degrees, refracted angle i think is =90degrees. i know that, , sin (theta).critical = n2/n1.

Water is 1.33
air is 1.0003

Not sure on where to start.
 
  • #4
The angle of reflection is equal to the angle of incidence. The problem statement states that the angle between the reflected and refracted rays is 90 degrees. That should be enough to solve it from there.
 
  • #5
N2 and THeta 2, s (1.003)water sin 90?

ANd N.1 sing theta1, = N1 sin ().1 = (1)sin THeta2, solve for n1??

i need the steps I am confused, trying to draw it out, but i get angle of incident
comng in, perpendicular . and angle of refraction on the right side. Both having
angles of 90 degrees.

Now to find criticle angle, its n2/n1 correct?
 
  • #6
Why are you assuming water?
 
  • #7
I guess i assumed, because
i was up at 2:30am, and was
confused :), sorry
 
  • #8
Yeah, the question seems to be asking you to figure out the angles of reflection and refraction and use these to find the index of refraction (parts (a) and (b)).
 
  • #9
Here the angle of incidence, i = 53 degree.whenever reflection takes place the angle of reflection will be equal to the angle of incidence.then the angle of reflection = 53 degree.
The angle between the reflected and the refracted ray = 90 degree
Therefore the angle between the refracted ray and the normal =the angle of refraction ,r = 180 - (53+90) = 180 -143 =37 degree.
A) = 37 degree.

B) Refractive index = sin i/sin r = sin 53/ sin 37 = 1.326
C) refractive index = 1/sin C ,where C is the critical angle or sin C =1/refractive index = 1/1.326 = 1/1.326 =0.7543
or C = sin inverse 0.7543 =48 degree 57 minutes.

does this make sense or this:

a)
Angle of refraction = 90° - 53° = 47°

b)
Refractive index
= sin(angle of incidence) / sin(angle of refraction)
= sin 53° / sin 47°
= 1.092.

c)
Critical angle
= sinֿ¹ (1 / 1.092)
= 66.3°.
 
  • #10
Pay attention to how we reference the angles for incidence, reflection, and refraction in terms of the normals. The angles are always right angles or acute, as shown in the reflection and refration sections of Wikipedia's Gemetrical Optics page: http://en.wikipedia.org/wiki/Geometrical_optics . So draw a diagram of the problem, the angle between the refracted and reflected rays is 90 degrees. Use this to figure out the relationship of the refracted ray to calculated it's angle with the normal inside the second medium.
 

1. What is refraction in geometric optics?

Refraction is the bending of light as it passes through different mediums, such as air, water, or glass.

2. How does refraction affect the path of light rays?

When light passes through a medium with a different density, the speed of the light changes, causing the light rays to bend. This change in direction is known as refraction.

3. How is the angle of refraction related to the angle of incidence?

The angle of refraction is determined by 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 speed of light in the first medium to the speed of light in the second medium. In simpler terms, the angle of refraction is directly related to the angle of incidence.

4. What is the difference between a reflected ray and a refracted ray?

A reflected ray is a ray of light that bounces off a surface and changes direction, while a refracted ray is a ray of light that passes through a surface and bends. Reflection occurs when the light hits a surface at a certain angle, while refraction occurs when the light passes through a medium with a different density.

5. How does Snell's law explain the behavior of light in refraction?

Snell's law mathematically describes the relationship between the angle of incidence and the angle of refraction when light passes through two different mediums. It helps us understand how light bends and changes direction as it passes through different materials, allowing us to predict the path of light rays in different situations.

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