$A$ glass cube of length $24 \ cm$ has a small air bubble trapped inside. When viewed normally from one face,it is $10 \ cm$ below the surface. When viewed normally from the opposite face,its apparent distance is $6 \ cm$. The refractive index of glass is:

When light travels from one medium to another with a different refractive index, which of the following will change?

$A$ rectangular block is composed of three different glass prisms (with refractive indices $\mu_1, \mu_2$ and $\mu_3$) as shown in the figure below. $A$ ray of light incident normal to the left face emerges normal to the right face. Then,the refractive indices are related by

$A$ glass slab consists of thin uniform layers of progressively decreasing refractive indices $(RI)$ such that the $RI$ of any layer is $\mu - m \Delta \mu$. Here, $\mu$ and $\Delta \mu$ denote the $RI$ of the $0^{\text{th}}$ layer and the difference in $RI$ between any two consecutive layers, respectively. The integer $m = 0, 1, 2, 3, \ldots$ denotes the number of the successive layers. $A$ ray of light from the $0^{\text{th}}$ layer enters the $1^{\text{st}}$ layer at an angle of incidence of $30^{\circ}$. After undergoing the $m^{\text{th}}$ refraction, the ray emerges parallel to the interface. If $\mu = 1.5$ and $\Delta \mu = 0.015$, the value of $m$ is:

$A$ tank is filled with water to a height of $16 \text{ cm}$. Find the apparent depth of a needle lying at the bottom of the tank as measured by a microscope. The refractive index of water $(\mu_{w})$ is $\frac{4}{3}$. (in $\text{ cm}$)

$A$ beam of monochromatic light is refracted from vacuum into a medium of refractive index $1.5$. The wavelength of refracted light will be