When the same monochromatic ray of light travels through a glass slab and through water,the number of waves in a glass slab of thickness $6 \ cm$ is the same as in a water column of height $7 \ cm$. If the refractive index of glass is $1.5$,then the refractive index of water is:

The time required for the light to pass through a glass slab (refractive index $= 1.5$) of thickness $4 \,mm$ is ($c = 3 \times 10^{8} \,m/s$, speed of light in free space).

$A$ microscope is focussed on a coin lying at the bottom of a beaker. The microscope is now raised by $1 \,cm$. To what depth should water be poured into the beaker so that the coin is again in focus is ........ $cm$ (The refractive index of water is $\frac{4}{3}$ )

$A$ paraxial beam of light is converging towards a point $P$ on the screen. $A$ plane parallel sheet of glass of thickness $t$ and refractive index $\mu$ is introduced in the path of the beam. The convergence point is shifted by:

$A$ 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?

$A$ small pin fixed on a table top is viewed from above from a distance of $50 \, cm$. By what distance would the pin appear to be raised if it is viewed from the same point through a $15 \, cm$ thick glass slab held parallel to the table? Refractive index of glass $= 1.5$. Does the answer depend on the location of the slab?