$A$ tank is filled with water to a height of $12.5 \, cm$. The apparent depth of a needle lying at the bottom of the tank is measured by a microscope to be $9.4 \, cm$. If water is replaced by a liquid of refractive index $1.63$ up to the same height,what will be the apparent depth of the needle in $cm$?

$A$ light ray is incident on a glass slab at an angle of incidence of $60^o$. If the angle between the reflected ray and the refracted ray is $90^o$,what is the refractive index of the glass slab?

For a colour of light,the wavelength in air is $6000 \ \mathring A$ and in water,the wavelength is $4500 \ \mathring A$. Then the speed of light in water will be:

$A$ monochromatic light of frequency $5 \times 10^{14} \ Hz$ travelling through air is incident on a medium of refractive index $2$. What will be the wavelength of the refracted light (in $nm$)?

$A$ ray of monochromatic light is incident on the plane surface of separation between two media $X$ and $Y$ with angle of incidence $i$ in medium $X$ and angle of refraction $r$ in medium $Y$. The given graph shows the relation between $\sin i$ and $\sin r$. If $V_X$ and $V_Y$ are the velocities of the ray in media $X$ and $Y$ respectively,then which of the following is true?

Consider a light ray travelling in air incident into a medium of refractive index $\sqrt{2n}$. The incident angle is twice that of the refracting angle. Then,the angle of incidence will be