(a) (i) Define refractive index of a medium in terms of speed of light. (ii) Derive the relation for the refractive index ( μ ) of a prism in terms…

From the triangle QNR, $\displaystyle r_{1}+r_{2}+\angle \mathrm{QNR}=180^{\circ}$. Comparing these two equations: $\displaystyle r_{1}+r_{2}=\mathrm{A} \quad \ldots(1)$

The total deviation $\displaystyle \delta$ is the sum of the deviations at the two faces: $\displaystyle \delta=\mathrm{i}+\mathrm{e}-\mathrm{A} \quad \ldots(2)$

For $\displaystyle \delta=\delta_{m}$, $\displaystyle \mathrm{i}=\mathrm{e}$, which implies $\displaystyle r_{1}=r_{2}$. From ($\displaystyle 1$) and ($\displaystyle 2$): $\displaystyle r=\dfrac{\mathrm{A}}{2}$, $\displaystyle \mathrm{i}=\dfrac{\mathrm{A}+\delta_{m}}{2}$

Refractive index of the prism: $\displaystyle n_{21}=\dfrac{n_{2}}{n_{1}}=\dfrac{\sin \dfrac{\left(\mathrm{A}+\delta_{m}\right)}{2}}{\sin \dfrac{\mathrm{A}}{2}}$

Wavefront — it is the locus of points which oscillate in the same phase.

Let CE represent the tangent plane drawn from the point C to this sphere. Then $\displaystyle \mathrm{AE}=\mathrm{BC}=v \tau$

Considering the triangles EAC and BAC, they are congruent. Therefore the angles i and r would be equal.