Answer:
Use Fermat's principle to show that the critical angle for total internal reflection is given by sino --, where n index of refraction of the incident medium and the external medium is air. 5. Light is incident from air onto a flat boundary surface with a transparent material whose refractive index is n=1.54 Find the angle of incidence if by refraction the direction o light is deviated through an angle 0 = 19.8" with respect to the direction of incidence. 6. Light is incident in the air on air-glass interface. If the refractive of glass is 1.7, find the incident angle such that the transmission angle is half of the incidence angle. 7. A ray of monochromatic light is incident at 45 on an equilateral triangular glass prism (n=1.58). Calculate the angle at which the ray leaves the opposite face of the prism. 8. A ray is incident on one face of a equilateral triangular glass prism in air (see Figure 1). The angle of incidence is chosen so that the emerging ray also makes the same angle e with the normal to the opposite face. a) Show that the index of refraction n of the glass prism is given by sin ota sin where a is the vertex angle of the prism and is the deviation angle, i.e. the total angle through which the beam is turned in passing through the prism. (Under these conditions the deviation angle 8 has the smallest possible value, which is called the angle of minimum deviation.) b) Write the expression of the angle of Figure 1