When light is incident on a medium at an angle $i$ and refracted into a second medium at an angle $r$,the graph of $\sin i$ vs $\sin r$ is as shown. From this,one can conclude that:

$A$ light ray incident along a vector $\vec{AO}$ $(\vec{AO} = 2\hat{i} - 3\hat{j})$ emerges along a vector $\vec{OB}$ $(\vec{OB} = C\hat{i} - 4\hat{j})$ as shown in the figure. The value of $C$ is . . . . . . .

The refractive index of water with respect to air is $4/3$ and the refractive index of glass with respect to air is $3/2$. The refractive index of water with respect to glass is

$A$ boat has a green light of wavelength $\lambda = 500 \ nm$ on the mast. What wavelength would be measured and what colour would be observed for this light as seen by a diver submerged in water by the side of the boat? Given,$n_{w} = 4/3$.

$A$ beam of light has a small wavelength spread $\delta \lambda$ about a central wavelength $\lambda$. The beam travels in vacuum until it enters a glass plate at an angle $\theta$ relative to the normal to the plate,as shown in the figure. The index of refraction of the glass is given by $n(\lambda)$. The angular spread $\delta \theta'$ of the refracted beam is given by

$A$ tank is filled with benzene to a height of $120 \,mm$. The apparent depth of a needle lying at the bottom of the tank is measured by a microscope to be $80 \,mm$. The refractive index of benzene is: (in $.5$)