The velocity of light in diamond is $\left(\frac{5}{12}\right)$ times that in air. The velocity of light in water is $\left(\frac{3}{4}\right)$ times that in air. Find the angle of incidence for a ray of light travelling from water to diamond,given that the angle of refraction $r = 30^{\circ}$ and $\sin 30^{\circ} = \frac{1}{2}$.

$A$ large square container with thin transparent vertical walls and filled with water (refractive index $\mu = \frac{4}{3}$) is kept on a horizontal table. $A$ student holds a thin straight wire vertically inside the water at a distance of $12 \ cm$ from one of its corners,as shown in the figure. Looking at the wire from this corner,another student sees two images of the wire,located symmetrically on each side of the line of sight. The separation (in $cm$) between these images is:

The refractive indices of glass and water with respect to air are $3/2$ and $4/3$ respectively. The refractive index of glass with respect to water will be

If the wavelength of light in air is $4200\, \mathring A$,what will be the wavelength of light in water $(\mu = 4/3)$ in $\mathring A$?

An opaque sphere of radius $a$ is just immersed in a transparent liquid as shown in the figure. $A$ point source is placed on the vertical diameter of the sphere at a distance $a/2$ from the top of the sphere. One ray originating from the point source after refraction from the air-liquid interface forms a tangent to the sphere. The angle of refraction for that particular ray is $30^{\circ}$. The refractive index of the liquid is:

$A$ ray of light strikes a glass plate at an angle of $60^o$. If the reflected and refracted rays are perpendicular to each other,the index of refraction of the glass is: