# A ray through prism

A ray with angle of incidence 60° is passed through a prism of angle 15°.

To find the net deviation I know we just apply Snell’s law twice for the ray refracting while going in and while coming out. Here’s my doubt - we find $$r_1$$ (Angle of refraction 1) to be 30°, and $$r_2$$ can be found out with the help of the relation $$A=r_1+r_2$$ which we get as -15°, what is the significance of the minus sign?

• I'd really suggest you sketch the beam path and the prism. Apr 23, 2021 at 16:34
• Apr 23, 2021 at 22:52

It means that, given the axis you have chosen, there's a 15 degrees inclination in the opposite direction. Negative angles don't have any particular or strange meaning, you could as well say it's +345 degrees.

• What do you mean by axis and which direction is opposite? Apr 23, 2021 at 16:33
• When you're expressing angles, you're doing it from a specific axis. Generally we increased angles counterclockwise, and decrease them clockwise. The Y-axis, for example, is 90 degrees WITH RESPECT TO the X-axis. The negative sign just means it's 15 degrees clockwise :) Apr 23, 2021 at 16:36

It would be more understandable visually

This is what a prism with a normal angle looks like; notice the side of the 15°.

Now consider another prism that is a little thinner. You will notice that the 15° is measured from the OTHER SIDE OF THE RED LINE (normal).

This 15° is written as -15° while writing mathematically. So if you get a negative angle as the answer, then how we measure the angle with respect to the normal is reversed.