A large square container with thin transparent vertical walls and filled with water (refractive index $${4 \over 3}$$) is kept on a horizontal table. A student holds a thin straight wire vertically inside the water 12 cm from one of its corners, as shown schematically 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 as shown. The separation (in cm) between these images is ;

A monochromatic light is incident from air on a refracting surface of a prism of angle 75$$^\circ $$ and refractive index $${n_0} = \sqrt 3 $$. The other refracting surface of the prism is coated by a thin film of material of refractive index n as shown in figure. The light suffers total internal reflection at the coated prism surface for an incidence angle of $$\theta \le 60^\circ $$. The value of n² is .............

A planar structure of length L and width W is made of two different optical media of refractive indices n₁ = 1.5 and n₂ = 1.44 as shown in figure. If L >> W, a ray entering from end AB will emerge from end CD. CD only if the total internal reflection condition is met inside the structure. For L = 9.6 m, if the incident angle $$\theta $$ is varied, the maximum time taken by a ray to exit the plane CD is t $$ \times $$ 10^-9 s, where, t is ................

[Speed of light, c = 3 $$ \times $$ 10⁸ m/s]

Sunlight of intensity $$1.3$$ $$kW\,{m^{ - 2}}$$ is incident normally on a thin convex lens of focal length $$20$$ cm. Ignore the energy loss of light due to the lens and assume that the lens aperture size is much smaller than its focal length. The average intensity of light, in $$kW\,{m^{ - 2}},$$ at a distance $$22$$ cm from the lens on the other side is ___________.