$A$ plane glass slab is kept over a coloured word '$VIBGYOR$',where the colour of each letter corresponds to the colours in white light. The letter which appears least raised is

When a convex lens is placed above an empty tank, the image of a mark at the bottom of the tank, which is $45 \ cm$ from the lens, is formed $36 \ cm$ above the lens. When a liquid is poured in the tank to a depth of $40 \ cm$, the distance of the image of the mark above the lens is $48 \ cm$. The refractive index of the liquid is

$A$ vessel is filled with two different liquids which do not mix. One liquid is $40 \ cm$ deep with a refractive index of $1.6$,and the other is $30 \ cm$ deep with a refractive index of $1.5$. What is the apparent depth of the vessel when viewed normally (in $cm$)?

$A$ ray of light is incident normally on a glass slab of thickness $5 \ cm$ and refractive index $1.6$. The time taken by a ray to travel from the source of light to the surface of the slab is the same as the time taken to travel through the glass slab. The distance of the source from the surface is: (in $cm$)

The apparent depth of a needle lying at the bottom of a tank,which is filled with water of refractive index $1.33$ to a height of $12.5\,cm$,is measured by a microscope to be $9.4\,cm$. If water is replaced by a liquid of refractive index $1.5$ up to the same height,what distance would the microscope have to be moved to focus on the needle again (in $,cm$)?

$A$ ray of light is incident at an angle of incidence $60^{\circ}$ on a glass slab of refractive index $\sqrt{3}$. After refraction,the light ray emerges out from the other parallel face,and the lateral shift between the incident ray and the emergent ray is $4 \sqrt{3} \, cm$. The thickness of the glass slab is . . . $cm$.