### Video Transcript

A triangular prism has an apex angle of 45 degrees. The minimum angle of deviation of the prism is 55 degrees. What is the angle of incidence that corresponds to this angle of deviation? Answer to the nearest degree.

Here, we’re working with a prism, where the apex angle 𝐴 is equal to 45 degrees. Along with this, we’re told that when a ray of light passes through the prism, the smallest angle that this ray can be deviated — that’s this angle here — is equal to 55 degrees. And we’ll call this smallest angle 𝛼 zero. Knowing all this, we want to solve for the angle of incidence of this ray. That angle is shown here, and we’ve called it 𝜙 zero.

To solve for 𝜙 zero, we can recall a mathematical relationship between these three variables highlighted. Whenever a light ray passes through a prism with apex angle 𝐴, if that ray is deviated at the minimum possible angle — we’ve called that angle 𝛼 zero — then the angle of incidence 𝜙 zero of this ray equals 𝛼 zero plus 𝐴 all divided by two.

In our case, since we’re given values for 𝛼 zero and 𝐴, we can substitute those in and then solve for 𝜙 zero. 𝛼 zero, we know, is 55 degrees. 𝐴 is 45 degrees. 55 plus 45 is 100 so that overall 𝜙 zero is 50 degrees. To the nearest degree, this is the angle of incidence corresponding to the minimum angle of deviation for this prism.