In the Figure below, a circular laser beam of diameter d traveling horizontally to the right is incident on a prism with a refractive index n and an apex angle ?. The prism is making an angle ? with the vertical.

a. After the beam exits the prism, what would be its diameter d'?

b. If d = 1 mm, ? = 30 degrees, refractive index of the prism is 1.5 (surrounding medium is air with refractive index ? 1), plot the magnification of the beam, m = d'/d as ? is varied from - 40 degrees to 40 degrees (clockwise is positive).

c. At what value of ?, is the magnification m = 2?

d. Using the principle of reversibility of light, explain how should you place the prism such that the magnification is m = ?

e. A second identical prism is placed next to the first prism at an angle ? as shown in figure 2. If ? = 30? . ? = 34.6?, ? = ?1.8? (clockwise is positive) and refractive index ? = 1.75, what is the angle of the final beam with respect to the initial beam (?)? Argue how this two-prism configuration can be used to convert an elliptical laser beam into a circular beam. [Many lasers such as external cavity diode lasers or ECDLs produce elliptical beams. It is often desirable to convert the elliptical beam to a circular beam for many reasons, such as to efficiently couple the light into an optical fiber.

a d n IBI Vertical line\f