$A$ microscope is focused on an object at the bottom of a bucket. If liquid with refractive index $\mu = \frac{5}{3}$ is poured inside the bucket,then the microscope has to be raised by $30\,cm$ to focus the object again. The height of the liquid in the bucket is $..........\,cm$.

The figure shows a ray of light entering and passing through a dense glass slab and emerging from the other side. If the angle of incidence $i=60^{\circ}$,slab thickness $b=0.04 \text{ m}$,and the refractive index of glass $\mu=\sqrt{3}$,the parallel shift $d$ between the emerging and entering rays in $\text{mm}$ is:

An ink mark is made on a piece of paper. $A$ glass slab of thickness $t$ is placed on it. The ink mark appears to be raised up through a distance $x$ when viewed at nearly normal incidence. If the refractive index of the material of the glass slab is $\mu$,then the thickness of the glass slab $t$ is given by:

An object is placed $20 \ cm$ in front of a $4 \ cm$ thick plane mirror. The image of the object is finally formed at $45 \ cm$ from the object itself. The refractive index of the material of the unpolished side of the mirror is (considering near normal incidence):

$A$ light wave is incident normally on a glass slab of refractive index $1.5$. If $4\%$ of light gets reflected and the amplitude of the electric field of the incident light is $30\, V/m$,then the amplitude of the electric field for the wave propagating in the glass medium will be.......$ V/m$

In determining the refractive index of a glass slab using a travelling microscope,the following readings are tabulated:
$(a)$ Reading of travelling microscope for ink mark $= 5.123 \ cm$
$(b)$ Reading of travelling microscope for ink mark through glass slab $= 6.123 \ cm$
$(c)$ Reading of travelling microscope for chalk dust on glass slab $= 8.123 \ cm$
From the data,the refractive index of a glass slab is: