$A$ flat glass slab of thickness $6\, cm$ and refractive index $1.5$ is placed in front of a plane mirror. An observer is standing behind the glass slab and looking at the mirror. The actual distance of the observer from the mirror is $50\, cm$. The distance of his image from himself,as seen by the observer is .......$cm$.

Two light rays initially in the same phase travel through two media of equal length $L$ having refractive indices $\mu_1$ and $\mu_2$ (where $\mu_1 > \mu_2$) as shown in the figure. If the wavelength of the light rays in air is $\lambda$,the phase difference of the emerging rays is given by:

$A$ 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:

The bottom of a container is a glass slab of thickness $4 \ cm$ and refractive index $\mu = 1.5$. The container contains two immiscible liquids $A$ and $B$ of depths $6 \ cm$ and $8 \ cm$ respectively. When a crack at the bottom surface of the glass slab is viewed from above,by what distance (in $cm$) does it appear to be shifted? The refractive indices of $A$ and $B$ are $1.4$ and $1.3$ respectively.

$A$ container contains a liquid with refractive index of $1.2$ up to a height of $60 \ cm$ and another liquid having refractive index $1.6$ is added to height $H$ above the first liquid. If viewed from above,the apparent shift in the position of the bottom of the container is $40 \ cm$. The value of $H$ is . . . . . . $\ cm$. (Consider liquids are immiscible)

One side of a glass slab is silvered as shown. $A$ ray of light is incident on the other side at an angle of incidence $i = 45^o$. The refractive index of the glass is $1.5$. The deviation of the ray of light from its initial path when it comes out of the slab is......$^o$.