$A$ 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

Obtain the relation between the real depth and apparent depth of the bottom of a tank filled with water when observed from air.

$A$ vessel of depth $d$ is half filled with oil of refractive index $n_1$ and the other half is filled with water of refractive index $n_2$. The apparent depth of this vessel when viewed from above will be

$A$ coin is placed at the bottom of a glass slab of refractive index $3$ and thickness $x$. Another glass slab of refractive index $\mu$ and thickness $x$ is placed on top of it. If the coin appears to be at the interface of the two slabs,then $\mu = $ . . . . . .

$A$ 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 $20 \%$. The angle of deviation is

$A$ convex lens is placed $10\, cm$ from a light source and it forms a sharp image on a screen,kept $10\, cm$ from the lens. Now,a glass block (refractive index $\mu = 1.5$) of $1.5\, cm$ thickness is placed in contact with the light source. To get the sharp image again,the screen is shifted by a distance $d$. Then $d$ is: