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

$A$ monochromatic light wave is incident normally on a glass slab of thickness $d$,as shown in the figure. The refractive index of the slab increases linearly from $n_1$ to $n_2$ over the height $h$. Which of the following statement$(s)$ is (are) true about the light wave emerging out of the slab?

$A$ layer of oil $3\,cm$ thick is floating on a layer of coloured water $5\,cm$ thick. The refractive index of coloured water is $5/3$ and the apparent depth of the two liquids appears to be $36/7\,cm$. Find the refractive index of oil.

$A$ ray of light is incident on a parallel slab of thickness $t$ and refractive index $n$. If the angle of incidence $\theta$ is small,then the lateral displacement between the incident and emergent ray will be

$A$ 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:

$A$ concave mirror is placed over a beaker containing water of refractive index $\mu = 1.33$. The object is placed at the bottom of the beaker. If the image of the object is formed at a distance of $25 \, cm$ from the top surface of the water,and the mirror is at a height of $15 \, cm$ above the water surface,find the focal length of the mirror in $cm$.