$A$ fish in water (refractive index $n$) looks at a bird vertically above in the air. If $y$ is the height of the bird and $x$ is the depth of the fish from the surface,then the distance of the bird as estimated by the fish is

The ratio of the refractive index of red light to blue light in air is

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 $1 \ m$.

$A$ circular disc of radius $R$ is placed co-axially and horizontally inside an opaque hemispherical bowl of radius $a$ (See figure). The far edge of the disc is just visible when viewed from the edge of the bowl. The bowl is filled with a transparent liquid of refractive index $\mu$ and the near edge of the disc becomes just visible. How far below the top of the bowl is the disc placed?

Light enters from air into a given medium at an angle of $45^{\circ}$ with the interface of the air-medium surface. After refraction,the light ray is deviated through an angle of $15^{\circ}$ from its original direction. The refractive index of the medium is

When light travels from glass to air,the incident angle is ${\theta _1}$ and the refracted angle is ${\theta _2}$. The true relation is: