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

The time taken by sunlight to cross a $5 \,mm$ thick glass plate $(\mu = 3/2)$ is

$A$ light ray is incident on a glass slab of thickness $4 \sqrt{3} \text{ cm}$ and refractive index $\sqrt{2}$. The angle of incidence is equal to the critical angle for the glass slab with air. The lateral displacement of the ray after passing through the glass slab is . . . . . . $\text{cm}$. (Given $\sin 15^{\circ} = 0.25$)

$A$ beaker contains water up to a height of $h_1$ and kerosene above the water up to a height of $h_2$. The total height is $(h_1 + h_2)$. The refractive index of water is $\mu_1$ and that of kerosene is $\mu_2$. What is the apparent shift of the bottom of the beaker when viewed from above?

$A$ bird is looking at a fish underwater from the air. $h_1$ is the height of the bird above the water surface and $h_2$ is the depth of the fish below the water surface. If $\mu$ is the refractive index of water with respect to air,then the distance of the fish as observed by the bird is:

When the same monochromatic ray of light travels through a glass slab and through water,the number of waves in a glass slab of thickness $6 \ cm$ is the same as in a water column of height $7 \ cm$. If the refractive index of glass is $1.5$,then the refractive index of water is: