$A$ monochromatic beam of light passes from a denser medium into a rarer medium. As a result,

Figures $(a)$ and $(b)$ show refraction of a ray in air incident at $60^{\circ}$ with the normal to a glass-air and water-air interface,respectively. Predict the angle of refraction in glass when the angle of incidence in water is $45^{\circ}$ with the normal to a water-glass interface [Figure $(c)$].

In the figure below,$PQRS$ denotes the path followed by a ray of light as it travels through three media in succession. The absolute refractive indices of the media are $\mu_1, \mu_2$ and $\mu_3$,respectively. (The line segment $RS$ in the figure is parallel to $PQ$). Then,

Give one example of a substance whose mass density is low but optical density is high.

In finding out the refractive index of a glass slab,the following observations were made through a travelling microscope: $50$ vernier scale divisions $= 49$ $MSD$; $20$ divisions on the main scale in each $cm$. For a mark on paper:
$MSR = 8.45 \ cm, VC = 26$
For the mark on paper seen through the slab:
$MSR = 7.12 \ cm, VC = 41$
For a powder particle on the top surface of the glass slab:
$MSR = 4.05 \ cm, VC = 1$
($MSR =$ Main Scale Reading,$VC =$ Vernier Coincidence)
The refractive index of the glass slab is:

When light travels from glass to air,the incident angle is ${\theta _1}$ and the refracted angle is ${\theta _2}$. The true relation is: