Monochromatic Light and a 30-60-90 Prism Problem

[hawaldko]

Homework Statement

Red light is incident in air on a 30o - 60o - 90 o prism as shown. The incident beam is directed at an angle of φ1 = 34.3o with respect to the horizontal and enters the prism at a height h = 26 cm above the base. The beam leaves the prism to the air at a distance d = 77.2 along the base as shown.

http://imgur.com/O9jZg

Image link: http://imgur.com/O9jZg

Homework Equations

Snell's Law

The Attempt at a Solution

So basically, I am getting really hung up with the geometry. I just can't figure out how to find angle 2. I've tried a couple of different triangles, and every useful one I come up with I can't solve and everyone I can solve, doesn't give me anything useful. My teacher said: "My suggestion is to focus on finding the second angle using geometry. My hint is to focus on h, which represents the distance from the point where the beam enters the prism to the bottom of the prism." I have literally been working on this for the past 2 days and I can't see what triangle to use.

 

[fishspawned]

please show the work you've completed so far.

 

[hawaldko]

http://imgur.com/eSiX2,PXl3b

http://imgur.com/eSiX2,PXl3b#1

 

[fishspawned]

ok what you need to do first is work out your angles. and you are not doing it correctly right now. refer to this image:

http://upload.wikimedia.org/wikipedia/commons/thumb/3/3f/Snells_law2.svg/334px-Snells_law2.svg.png

and make sure you are using the correct angles - make note that the normal line is perpendicular to the surface. this is important when figuring out your first angle.

 

[asteriatic]

As a scientist, it is important to approach problems with a systematic and analytical mindset. In this case, the key to solving this problem is to use Snell's Law, which relates the angle of incidence and refraction to the refractive indices of the materials involved.

To find angle 2, we can use the fact that the incident and refracted rays are parallel, and therefore, the angles of incidence and refraction are equal. We can also use the fact that the incident and refracted rays form a right angle with the base of the prism.

Using these conditions, we can construct a right triangle with the hypotenuse being the incident ray, one side being the refracted ray, and the other side being the base of the prism. This will allow us to use trigonometric functions to solve for angle 2.

We can also use the given information about the incident angle and the height of the incident ray to find the length of the base of the triangle. This will help us calculate the angle 2 using trigonometric functions.

Once we have found angle 2, we can use Snell's Law to find the refractive index of the prism material. From there, we can use the refractive index to find the angle of refraction and finally, the angle of incidence.

Overall, it is important to approach this problem with a clear understanding of the physical principles involved and to use a systematic approach to solving it. With careful analysis and the use of appropriate equations, we can find the solution to this problem.