$A$ beam of white light is partially reflected and partially refracted from a surface. The angle between the reflected and refracted light is $90^{\circ}$. The angle of refraction is $30^{\circ}$. The angle of incidence must be (in $^{\circ}$)

$A$ boat has a green light of wavelength $\lambda = 500 \ nm$ on the mast. What wavelength would be measured and what colour would be observed for this light as seen by a diver submerged in water by the side of the boat? Given,$n_{w} = 4/3$.

Shown in the figure is a transparent tank of length $30 \,cm$. $A$ black strip of width $3.8 \,cm$ is stuck on its left wall. When a source of light is kept to the left of it,a shadow of width $7.6 \,cm$ is formed on the right wall. Now,the tank is filled with a liquid of refractive index $n$,and the width of the shadow reduces to $6.4 \,cm$. The value of $n$ is closest to

$A$ glass cube of length $24 \ cm$ has a small air bubble trapped inside. When viewed normally from one face,it is $10 \ cm$ below the surface. When viewed normally from the opposite face,its apparent distance is $6 \ cm$. The refractive index of glass is:

Optical phenomena taking place for a mirror and a lens respectively are . . . . . . and . . . . . . .

$A$ light beam is traveling from Region $I$ to Region $IV$ (Refer Figure). The refractive indices in Regions $I, II, III$ and $IV$ are $n_0, \frac{n_0}{2}, \frac{n_0}{6}$ and $\frac{n_0}{8}$,respectively. The angle of incidence $\theta$ for which the beam just misses entering Region $IV$ is: