The figure shows a surface $XY$ separating two transparent media, medium -$1$ and medium -$2$. The lines $a b$ and cd represent wavefronts of a light wave travelling in medium-$1$ and incident on $XY$. The lines ef and gh represent wavefronts of the light wave in medium-$2$ after refraction.

$Image$

$1.$  Light travels as a

$(A)$ parallel beam in each medium

$(B)$ convergent beam in each medium

$(C)$ divergent beam in each medium

$(D)$ divergent beam in one medium and convergent beam in the other medium.

$2.$  The phases of the light wave at $\mathrm{c}, \mathrm{d}, \mathrm{e}$ and $\mathrm{f}$ are $\phi_{\mathrm{c}}, \phi_{\mathrm{d}}, \phi_{\mathrm{e}}$ and $\phi_{\mathrm{f}}$ respectively. It is given that $\phi_{\mathrm{c}} \neq \phi_{\mathrm{f}}$

$(A)$ $\phi_{\mathrm{c}}$ cannot be equal to $\phi_{\mathrm{d}}$

$(B)$ $\phi_{\mathrm{a}}$ can be equal to $\phi_{\mathrm{e}}$

$(C)$ $\left(\phi_{\mathrm{d}}-\phi_t\right)$ is equal to $\left(\phi_{\mathrm{c}}-\phi_{\mathrm{e}}\right)$

$(D)$ $\left(\phi_{\mathrm{d}}-\phi_c\right)$ is not equal to $\left(\phi_{\mathrm{f}}-\phi_e\right)$

$3.$  Speed of the light is

$(A)$ the same in medium-$1$ and medium-$2$

$(B)$ larger in medium-$1$ than in medium-$2$

$(C)$ larger in medium-$2$ than in medium-$1$

$(D)$ different at $\mathrm{b}$ and $\mathrm{d}$

Give the answer question $1, 2$ and $3.$

The wave theory of light was given by

Wave front is locus of all the points where the particles of the medium vibrate with the same

Huygen wave theory allows us to know

Write the limitation of Huygen's principle.