$A$ glass slab of thickness $3 \ cm$ is placed on an ink mark on a piece of paper. For a person looking at the mark from a distance of $5.0 \ cm$ above the top surface of the slab, the mark appears to be at a distance of $4.0 \ cm$ from the observer. The refractive index of the 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

$A$ small pin fixed on a table top is viewed from above from a distance of $50 \, cm$. By what distance would the pin appear to be raised if it is viewed from the same point through a $15 \, cm$ thick glass slab held parallel to the table? Refractive index of glass $= 1.5$. Does the answer depend on the location of the slab?

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:

Consider three media $P$, $Q$, and $R$ with refractive indices $1$, $1.25$, and $1.5$, respectively. The medium $Q$ having a thickness of $5 \text{ cm}$ is placed between extended media $P$ and $R$. An object $O$ is placed at the centre of medium $Q$. If viewed from medium $P$ near the normal direction, the apparent depth of $O$ is $h_1$. For similar observation from medium $R$, the apparent depth is $h_2$. The value of $|h_1 - h_2|$, in $\text{cm}$, is:

$A$ tiny air bubble in a glass slab $(\mu = 1.5)$ appears from one side to be $6 \, cm$ from the glass surface and from the other side,$4 \, cm$. The thickness of the glass slab is......$cm$