Trigonometry Help: Calculating the Angle of Light Entry & Exit

In summary, the conversation discusses a problem with finding the angle at which light enters and exits a prism using Snell's law. The person is struggling to find the correct angle and is unsure about the concept of the normal to a surface. Through the conversation, it is determined that the angle between the laser and the dotted line (perpendicular to the flat side of the triangle) can be found by taking pi/2 minus the angle between the ray and the surface. The conversation also guides the person to draw a diagram and use geometric relationships to find the correct angle.
  • #1
JoeyBob
256
29
Homework Statement
See attached
Relevant Equations
Snell's law
So what I did first was made the face of the triangle flat and calculated the angle the light entered it. This means the light enters the triangle from the base corner angle (so (180-38.8)/2) of 70.6 degrees.

1sin(70.6)=1.47sin(angle)

angle=39.915

Now I need to find the angle it exits. But this part doesn't make sense to me because Ill just be left with my original angle.

1.47sin(39.915)=sin(angle)

angle=70.6 degrees

The answer is suppose to be 20.3. I am obviously messing up with the geometry of the problem though I am not sure how. Trigonometry I was never good at.
 

Attachments

  • question.PNG
    question.PNG
    8.1 KB · Views: 78
Physics news on Phys.org
  • #2
JoeyBob said:
Homework Statement:: See attached
Relevant Equations:: Snell's law

So what I did first was made the face of the triangle flat and calculated the angle the light entered it. This means the light enters the triangle from the base corner angle (so (180-38.8)/2) of 70.6 degrees.

1sin(70.6)=1.47sin(angle)

angle=39.915

Now I need to find the angle it exits. But this part doesn't make sense to me because Ill just be left with my original angle.

1.47sin(39.915)=sin(angle)

angle=70.6 degrees

The answer is suppose to be 20.3. I am obviously messing up with the geometry of the problem though I am not sure how. Trigonometry I was never good at.
In the standard form of Snell's law, the angles are to the normal. Does it look like the ray enters at 70 degrees to the normal?
 
  • #3
haruspex said:
In the standard form of Snell's law, the angles are to the normal. Does it look like the ray enters at 70 degrees to the normal?
The normal? Are you saying it entered at 0 degrees?
 
  • #4
JoeyBob said:
The normal? Are you saying it entered at 0 degrees?
By normal, I mean the normal to the surface the ray is passing through. The diagram shows the normal as a dotted line.
What is the angle the ray makes to that on entry?
 
  • #5
haruspex said:
By normal, I mean the normal to the surface the ray is passing through. The diagram shows the normal as a dotted line.
What is the angle the ray makes to that on entry?
Im not sure, that's what's making me not get the answer. would be 180-38.8 then divided by 2 = 70.6

This would be the angle at each bottom corner. And if I rotate the tringle so the side the light hit is flat, its a rotation of 70.6 degrees.
 
  • #6
JoeyBob said:
180-38.8 then divided by 2 = 70.6
That gives you the angle the base of the prism makes to each side of the prism. Since the ray comes parallel to the base, it is also the angle between the ray and the side of the prism.
But you want the angle between the ray and the normal to the side of the prism.
 
  • #7
haruspex said:
That gives you the angle the base of the prism makes to each side of the prism. Since the ray comes parallel to the base, it is also the angle between the ray and the side of the prism.
But you want the angle between the ray and the normal to the side of the prism.
How do I do that or where can I read about how to find the normal?
 
  • #8
JoeyBob said:
How do I do that or where can I read about how to find the normal?
Normal to a surface means at right angles to it. If the ray is at angle θ to the surface then it is at angle π/2-θ to the normal..
 
  • #9
haruspex said:
Normal to a surface means at right angles to it. If the ray is at angle θ to the surface then it is at angle π/2-θ to the normal..

Yes, the angle is between the laser and the dotted line (perpendicular to the flat side of the triangle). I understand that, but I don't know how to find such an angle.

So your saying its pi/2-angle, but what angle?
 
  • #10
JoeyBob said:
Yes, the angle is between the laser and the dotted line (perpendicular to the flat side of the triangle). I understand that, but I don't know how to find such an angle.

So your saying its pi/2-angle, but what angle?
Draw the prism.
Point A is the apex of the prism, B the lower left corner and C is the lower right corner.
What is the value of angle ABC?
Point E is where the ray hits the prism. D is where the ray has come from.
Draw line DE.
What is the geometric relationship between lines DE and BC?
What is the value of the angle DEB?
Line FE is the normal to the prism at point E.
What is angle FEB?
So what is angle FED?
 

1. What is trigonometry?

Trigonometry is a branch of mathematics that deals with the relationships between the sides and angles of triangles. It is commonly used in fields such as engineering, physics, and astronomy to solve problems involving angles and distances.

2. How is trigonometry used to calculate the angle of light entry and exit?

Trigonometry can be used to calculate the angle of light entry and exit by using the properties of right triangles. The angle of light entry can be found by using the tangent function, while the angle of light exit can be found by using the sine or cosine function.

3. What is the difference between the angle of light entry and exit?

The angle of light entry is the angle at which light enters a medium, while the angle of light exit is the angle at which light leaves the medium. These angles are related by Snell's Law, which states that the ratio of the sines of the angles of incidence and refraction is equal to the ratio of the velocities of light in the two media.

4. How does the angle of light entry and exit affect the path of light?

The angle of light entry and exit can greatly affect the path of light. If the angle of entry is greater than the critical angle, the light will be reflected back into the medium. If the angle of entry is less than the critical angle, the light will be refracted and continue through the medium. The angle of exit determines the direction of the refracted light.

5. What are some real-world applications of calculating the angle of light entry and exit?

Calculating the angle of light entry and exit is important in many fields, including optics, astronomy, and photography. It is used to determine the path of light through lenses and mirrors, the refraction of light through different media, and the angles of celestial objects in the sky. It is also used in the design of cameras and telescopes to ensure proper focus and image quality.

Similar threads

Calculating distance of Mars from the Sun based on two elongations
    • Introductory Physics Homework Help
Replies
2
Views
606
Refraction through different mediums: calculating multiple angles help
    • Introductory Physics Homework Help
Replies
6
Views
973
Calculating Incidence Angle for Tilted Plate and Light Source
    • Introductory Physics Homework Help
Replies
4
Views
1K
A Optimum profile of light pipe exit for narrow beam angle
    • Optics
Replies
16
Views
942
What Angle Does Light Emerge from a Prism?
    • Introductory Physics Homework Help
Replies
4
Views
2K
Calculating the Depth of a Cylinder Using Refraction
    • Introductory Physics Homework Help
Replies
7
Views
2K
Effects of changing the angle on an inclined plane
    • Introductory Physics Homework Help
Replies
1
Views
2K
Angle Spread with Snell's Law
    • Introductory Physics Homework Help
Replies
10
Views
7K
I Formula For Calculating Field Angle (Beam Angle) of Light?
    • General Math
Replies
2
Views
1K
Triangle Math Help: Calculate Angles & Lengths with 46 & 35 Measurements
    • Precalculus Mathematics Homework Help
Replies
11
Views
873

Hot Threads

Recent Insights

Back
Top