A fish rising vertically up towards the surface of water with speed 3 ms–1 and a bird diving vertically down towards it with speed 9 ms–¹. The velocity of bird with respect to fish and velocity of fish with respect to bird will be :

A small fish 0.4m below the surface of a lake , is viewed through a simple converging lens of focal length 3m. The lens is kept at 0.2 m above the water surface such that fish lies on the optical axis of the lens. The image of the fish seen by observer will be at \[v\]

A prism (μ = 1.5) has refracting angle of 30°. The deviation of a monochromatic ray incident normally on its one surface will be : –
(sin 48° 36′ = 0.75)

A ray falls on a prism ABC (AB = BC) and travels as shown in figure. The minimum refractive index of the prism material should be

A thin equiconvex glass lens of focal length 10 cm is cut and separated and a material of refractive index 3 is filled between them. What is the focal length of the combination ?
\[\left( \mu_{glass}=1.5\right)\]

Match the correct u-v graph with optical system using Cartesian sign conventions :

For the situations shown in the figure, determine the angle by which the mirror should be rotated, so that the light ray will retrace its path after refraction through the prism and reflection from the mirror ?

A ray of light falls on a transparent sphere with centre at C as shown in fig.

The ray emerges from the sphere parallel to line AB. The refractive index of the sphere is