Understanding Prism Deviation Angle in Optics

[Shamim]

1. Dear all
Hello
My name is Shamim and I am a student in high school and having 15 years old. I am a newcomer in this forum. I have found this great forum from internet while I was searching into that. I am really interested too much to physics and actually trying to learn more about that. I wish I can learn this subject as well as I can and learn a lot from you all dear friends.
This is my first question in this forum. I hope you dear experts can help me and giving me some advise?
Here there is a prism that a light is going through the prism (thick space) from air (thin space). So because of difference density space the light being broken into the prism and again gets broken from prism to thin space (air). If we length the lines from the light from where is coming inside prism and from where it is going out we will make an angle that it shows deviation angle and it gives us a formula as below, according the book said, that I have:

2. (D= I + r’ – A)[/b]
3. Unfortunately I couldn’t demonstrate for myself this formula. Would you please advise me?
I am thank you very very much in advance.

Best regards
Shamim

 

[ehild]

Hi Shamim, welcome to PF!
This is really a good place, but there are stick rules. We are not allowed to give full solution to you. And you need to show, what you tried and where you are stuck. Read https://www.physicsforums.com/showthread.php?t=686781, please.

You certainly have learned about triangles and you know that the sum of the interior angles is 180°. You also know what the exterior angles are and an exterior angle is equal to the sum of the two remote interior angles.
You might look at
http://www.wyzant.com/resources/lessons/math/geometry/triangles/angles_of_triangles

Now see the attached picture. Both the incident ray and the deflected ray are extended in the first picture. You get the blue triangle. Find how the angles of the triangle are related to i, r and i', r' and with the exterior angle D. In the second figure, the gray angles are 90°. You find a relation for A, r,, i'. Combining the equations obtained, you get the formula in the book.

ehild

 

[Shamim]

Dear ehild
So sorry Ok, from next time I do the same as you told. :shy: And thank you very very much for your kindness reply and your advise. Very useful to me.

Best regards
Shamim