$A$ needle is lying at the bottom of a water tank of height $12 \,cm$. The apparent depth of the needle measured by a microscope is $9 \,cm$. If the water is replaced by a liquid of refractive index of $1.5$ of same height, the distance through which the microscope has to be moved to focus the needle again is (in $\,cm$)

$A$ beaker containing liquid is placed on a table,underneath a microscope which can be moved along a vertical scale. The microscope is focused,through the liquid,onto a mark on the table when the reading on the scale is $a$. It is next focused on the upper surface of the liquid and the reading is $b$. More liquid is added and the observations are repeated; the corresponding readings are $c$ and $d$. The refractive index of the liquid is

Explain rarer and denser medium.

$A$ medium shows the relation between $\sin i$ and $\sin r$ as shown in the graph. If the speed of light in the medium is $nc$,then the value of $n$ is:

The ratio of the refractive index of red light to blue light in air is

If ${ }_{i} \mu_{j}$ represents the refractive index when a ray goes from medium $i$ to medium $j$,then the product ${ }_2 \mu_1 \times { }_3 \mu_2 \times { }_4 \mu_3$ is equal to: