The figure shows a water column BCFE surrounded by two media

(1)

and ($\displaystyle 3$) of the same refractive index $\displaystyle \sqrt{2}$. A ray of light from a point source S is incident on surface BE at an angle of $\displaystyle 30$°.

(1)

(a)

Trace the path of ray through media ($\displaystyle 2$) and ($\displaystyle 3$) as it emerges out of face CG.

(b)

Find the angle of emergence at face CG.

Refraction from face CF $\displaystyle \frac{4}{3}$ Sin $\displaystyle \mathrm{r}=\sqrt{2}$ Sin $\displaystyle \mathrm{r}_{2}$ $\displaystyle \frac{4}{3} \times \frac{3}{4 \sqrt{2}}=\sqrt{2}$ Sin $\displaystyle \mathrm{r}_{2}$ $\displaystyle \mathrm{r}_{2}=30^{0}$ $\displaystyle \angle C+\angle C R S+\angle C S R=180^{0}$ $\displaystyle 30^{\circ}+60^{\circ}+\angle C S R=180^{\circ}$ Ray goes perpendicularly out from face CG $\displaystyle \mathrm{e}=0$ ∴ Ray RS incidents perpendicular to CS ∴ angle of emergence of the ray is zero. Alternatively- As medium is same on both side of the water column. Angle of emergence Now $\displaystyle \mathrm{r}_{2}=30^{0}$ $\displaystyle \mathrm{r}_{1}+30=30$ $\displaystyle \mathrm{r}_{1}=0, \quad$ Hence $\displaystyle \mathrm{e}=0$