How Do You Find the Angle of Incidence from a Prism to Air?

[totomyl]

Homework Statement

it is the third question:

Attempt

Here is my attempt at the question, i got up to the point where i need to find the angle of incidence from the prism to the air, but i don't know how to do that. The solution page says to use 60^o minus the angle of refraction i just calculated, but i don't know why we need to do that.

if you could please tell me why we use that or how we get the angle from the prism to the air, that would be very helpful. thank you.

 

[kuruman]

The statement of the problem does not match the numbers that you are using. Setting that aside, you can find the angle of incidence by bringing into the picture the upper triangle formed by the top apex of the prism, by the point where the ray enters the prism and the point where it exits the prism. You already know that one angle is 60^o. You can relate the other two angles to the angle of refraction, which you already know, and the exit of angle that is the unknown.

 

[gneill]

An alternative method is to note that the two normals meet in the interior of the prism at an angle of 120°. Use the triangle Δabc formed by the normals and the light ray.

 

[totomyl]

An alternative method is to note that the two normals meet in the interior of the prism at an angle of 120°. Use the triangle Δabc formed by the normals and the light ray.

View attachment 106850

could i ask how you got the 120 when both of the normals meet? this is where my geometry skills come in i assume.

 

[gneill]

could i ask how you got the 120 when both of the normals meet? this is where my geometry skills come in i assume.

Yes. It's just a matter of transferring angles around various reference lines and intersections. Erect a few verticals to create triangles and reference lines. Use the fact that triangle angles sum to 180 and complimentary angles to 90. See if you can't "transfer" the prism's base angles to where b is in the diagram (erect a vertical through b to divide the angle there into two parts). Give it a try.

 

[J Hann]

From geometry what is the sum of the interior angles of a 4-sided figure?

 

[totomyl]

Yes. It's just a matter of transferring angles around various reference lines and intersections. Erect a few verticals to create triangles and reference lines. Use the fact that triangle angles sum to 180 and complimentary angles to 90. See if you can't "transfer" the prism's base angles to where b is in the diagram (erect a vertical through b to divide the angle there into two parts). Give it a try.

i see, thank you for the help i think i can work out the rest on my own now. this was very helpful and will be useful for future reference.