# Angle of deviation in a prism given ONLY the prism angle

This is NOT about calculating the minimum deviation of a prism. You are given only two pieces of information: the angle of the prism, the refractive index of the medium (glass), and you know that the input ray is horizontal (parallel to the base of the prism). The refractive index of the entry material is air, so refractive index is unity. Is it possible to derive the deviation of the beam in terms of prism angle without knowing the exact angle of incidence? I have been on a whiteboard scratching my head trying to derive this one...

• If you know the angle of the prism, and that the incident ray is parallel to the base, that tells you the angle of incidence. It's just geometry. Commented May 27, 2021 at 16:51
• @RogerJBarlow - The angle of incidence is measured normal to the material, so I am unsure how you could go from prism angle -> incidence Commented May 27, 2021 at 16:55
• Is the prism cross-section at least an isosceles triangle? Commented May 27, 2021 at 17:14
• @DJohnM No - consider it unknown Commented May 27, 2021 at 20:08
• This kind of optical prisms are always isosceles. If its not, there is not enough information for this problem. Commented May 27, 2021 at 22:33

Draw the perpendicular. The angles shown as $$a$$ are all equal
Hints: Line AB is straight, EDC is 90 degrees, CDB can be found in terms of $$\theta$$, so ADE can be got in terms of $$\theta$$ and that's the angle of incidence you need.