$A$ transparent cube of $15\, cm$ edge contains a small air bubble. Its apparent depth when viewed through one face is $6\, cm$ and when viewed through the opposite face is $4\, cm$. Then the refractive index of the material of the cube is

$A$ ray of light travelling through a rarer medium is incident at a very small angle '$i$' on a glass slab,and after refraction,its velocity is reduced by $25 \%$. The angle of deviation is:

An underwater swimmer is at a depth of $12 \, m$ below the surface of water. $A$ bird is at a height of $18 \, m$ from the surface of water,directly above his eyes. For the swimmer,the bird appears to be at a distance from the surface of water equal to ....... $m$ (Refractive index of water is $4/3$).

In determining the refractive index of a glass slab using a travelling microscope,the following readings are tabulated:
$(a)$ Reading of travelling microscope for ink mark $= 5.123 \ cm$
$(b)$ Reading of travelling microscope for ink mark through glass slab $= 6.123 \ cm$
$(c)$ Reading of travelling microscope for chalk dust on glass slab $= 8.123 \ cm$
From the data,the refractive index of a glass slab is:

$A$ ray of light is incident on a thick slab of glass of thickness $t$ as shown in the figure. The emergent ray is parallel to the incident ray but displaced sideways by a distance $d$. If the angles are small,then $d$ is

$A$ glass slab of thickness $3 \, cm$ and refractive index $3/2$ is placed on an ink mark on a piece of paper. The mark is viewed from a distance of $5.0 \, cm$ above the top surface of the slab. At what distance (in $cm$) will the mark appear to be?