$A$ thin oil layer floats on water. $A$ ray of light making an angle of incidence of $40^o$ shines on the oil layer. The angle of refraction of the light ray in water is......$^o$ $({\mu _{oil}} = 1.45, {\mu _{water}} = 1.33)$

Captain Jack Sparrow tries to observe a fish almost vertically below him in a magical sea of variable refractive index $\mu = y^2 + 1$,where $y$ is the depth below the water surface. Find the apparent depth of the fish below the water level as seen by Captain Jack Sparrow. The actual depth of the fish is $1 \ m$.

$A$ ray of light is incident at an angle $i$ on a glass slab of refractive index $\mu$. The angle between the reflected and refracted light is $90^{\circ}$. Then,the relationship between $i$ and $\mu$ is

An object is immersed in a fluid of refractive index $\mu$. In order that the object becomes invisible when observed from outside,it should

The refractive index of a certain glass is $1.5$ for light whose wavelength in vacuum is $6000\;\mathring A.$ The wavelength of this light when it passes through glass is.......$\mathring A.$

$A$ light ray is incident on a glass slab at an angle of incidence of $60^o$. If the angle between the reflected ray and the refracted ray is $90^o$,what is the refractive index of the glass slab?