Try it on paper first. A hint, the key idea and the worked solution are here when you need them.
A prism of angle is made of glass of refractive index . A student shines a narrow beam on one face and slowly turns the prism, so that the angle of incidence changes. At some angles the light comes out of the second face. At others it is reflected inside the glass and never leaves. The picture shows the smallest angle of incidence for which the ray just leaves, skimming along the second face. Find the critical angle of the glass. Find the largest prism angle for which any ray at all can come out of the second face. Find the smallest angle of incidence on the first face for which the ray comes out, and the angle of deviation then. Finally find the minimum deviation of this prism.
For a prism, and . At minimum deviation, and . For a thin prism, , and the dispersive power is . A ray can leave a face only if the angle inside is smaller than the critical angle, .
Have you tried it?
Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.
Given. and .
Step 1. The critical angle. , so .
Step 2. The largest prism angle. The angle cannot be larger than either, because and . So and . Since , we need .
Step 3. The smallest angle of incidence. The ray just leaves when . Then . Snell's law at the first face gives , so .
Step 4. The deviation there. At that moment , so .
Step 5. The minimum deviation. , so . Then , so .
Answer: , , , and .
Watch out. Smaller angles of incidence than give total internal reflection at the second face. The deviation is the largest deviation of any ray that comes out. The deviation then falls to and rises again, as in the graph of the lesson.
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