(a) Definition of wavefront Verifying laws of refraction by Huygen's principle (b) Polarisation by scattering Calculation of Brewster's angle (a) The wavefront is the common locus of all points which are in phase(surface of constant phase) Let a plane wavefront be incident on a surface separating two media as shown. Let $v_1$ and $v_2$ be the velocities of light in the rarer medium and denser medium respectively. From the diagram $\;BC=v_1 t\;\text{ and }\;AD=v_2 t$ $\; \sin i \;=\; \frac{BC}{AC} \;\text{ and }\; \sin r \;=\; \frac{AD}{AC}$ $\; \therefore \; \frac{\sin i}{\sin r} \;=\; \frac{BC}{AD} \;=\; \frac{v_1 t}{v_2 t}$ $\;=\; \frac{v_1}{v_2} a \;\text{ constant }\;$ This proves Snell's law of refraction. (b) When unpolarised light gets scattered by molecules, the scattered light has only one of its two components in it. (Also accept diagrammatic representation) $\; \text{We have,}\; \mu = \tan i_{B}$ $\therefore \tan i_{B} = 1.5$ $\therefore i_{B} = \tan^{-1} 1.5 = 56.3^{\circ}$ OR (a) Ray diagram Expression for power (b) Formula Calculation of speed of light Two thin lenses, of focal length $f_1$ and $f_2$ are kept in contact. Let $O$ be the position of object and let $u$ be the object distance. The distance of the image (which is at $I_1$ ), for the first lens is $v_1$. This image serves as object for the second lens. Let the final image be at I. We then have $\;\; \frac{1}{f_1} \;=\; \frac{1}{v_1} - \frac{1}{u}$ $\;\; \frac{1}{f_2} \;=\; \frac{1}{v} - \frac{1}{v_1}$ Adding, we get$\;\; \frac{1}{f_1} + \frac{1}{f_2} \;=\; \frac{1}{v} - \frac{1}{u} \;=\; \frac{1}{f}$$\; \therefore \; \frac{1}{f} \;=\; \frac{1}{f_1} + \frac{1}{f_2}$$\; P = P_1 + P_2$(b) At minimum deviation$r = \frac{A}{2} = 30^{\circ}$We are given that$\; i \;=\; \frac{3}{4} A = 45^{\circ}$$\; \therefore \; \mu = \frac{\sin 45^{\circ}}{\sin 30^{\circ}} = \sqrt{2}$$\therefore$ Speed of light in the prism $= \frac{c}{\sqrt{2}}$ $(\cong 2.1 \times 10^8 \text{ms}^{-1})$