What is the lateral shift of a ray refracted through a parallel-sided glass slab of thickness $h$ in terms of the angle of incidence $i$ and angle of refraction $r$,if the glass slab is placed in air medium?

$A$ fish at a depth of $12 \, cm$ in water is viewed by an observer on the bank of a lake. To what height is the image of the fish raised? (Refractive index of water $\mu = 4/3$)

$A$ vessel of depth $x$ is half filled with oil of refractive index $\mu_1$ and the other half is filled with water of refractive index $\mu_2$. The apparent depth of the vessel when viewed from above is

Time taken by the sunlight to pass through a window of thickness $4 \, mm$ whose refractive index is $1.5$ is

$A$ paraxial beam of light is converging towards a point $P$ on the screen. $A$ plane parallel sheet of glass of thickness $t$ and refractive index $\mu$ is introduced in the path of the beam. The convergence point is shifted by:

$A$ glass hemisphere of radius $0.04\, m$ and refractive index $1.6$ is placed centrally over a cross mark on a paper:
$(i)$ with the flat face in contact with the paper;
$(ii)$ with the curved face in contact with the paper.
In each case,the cross mark is viewed directly from above. The positions of the images will be: