$A$ coin is placed at the bottom of an empty beaker and is focused by a microscope. When water is poured into the beaker to a height of $10 \, cm$,how much must the microscope be moved to focus it again?

$A$ 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 $25 \%$. The angle of deviation is:

$A$ 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

$A$ light ray is incident on a glass slab of thickness $4 \sqrt{3} \text{ cm}$ and refractive index $\sqrt{2}$. The angle of incidence is equal to the critical angle for the glass slab with air. The lateral displacement of the ray after passing through the glass slab is . . . . . . $\text{cm}$. (Given $\sin 15^{\circ} = 0.25$)

$A$ 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 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 $cm$)

$A$ parallel-sided block of glass with a refractive index of $1.5$ and a thickness of $36 \, mm$ rests on the floor of a tank filled with water (refractive index $= 4/3$). The difference between the apparent depth of the floor at $A$ (where the glass block is present) and $B$ (where only water is present) when seen from vertically above is equal to $....... \, mm$.