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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?

Natru
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2 Answers2

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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.

MiguelFuego
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  • What do you mean by axis and which direction is opposite? – Natru Apr 23 '21 at 16:33
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    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 :) – MiguelFuego Apr 23 '21 at 16:36
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It would be more understandable visually

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

This is what a prism with a normal angle looks like, notice the 15 def

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).

Here is another prism with a smaller angle

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.

Natru
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