$A$ 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 $\sin 15^{\circ} = 0.25$)

$A$ slab of glass,of thickness $6\, cm$ and refractive index $1.5$,is placed in front of a concave mirror,the faces of the slab being perpendicular to the principal axis of the mirror. If the radius of curvature of the mirror is $40\, cm$ and the reflected image coincides with the object,then the distance of the object from the mirror is.....$cm$

An air bubble in a glass slab of thickness $15 \, cm$ appears to be at $6 \, cm$ from one side and at $4 \, cm$ from the opposite side. The refractive index of the glass is:

$A$ 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

Three immiscible liquids of densities $d_1 > d_2 > d_3$ and refractive indices $\mu_1 > \mu_2 > \mu_3$ are put in a beaker. The height of each liquid column is $\frac{h}{3}$. $A$ dot is made at the bottom of the beaker. For near normal vision,find the apparent depth of the dot.

$A$ plane glass slab is kept over various coloured letters. The letter which appears least raised is