Derive the laws of refraction from the concept (Huygen's principle) of the wavefront.
Derive the laws of refraction from the concept (Huygen's principle) of the wavefront.
According to Huygen's principle of wavefront is as follow.
Let PP' represent the surface separating medium-$1$ and medium-$2$, as shown in figure.
And $v_{1}$ and $v_{2}$ represent the speed of light in medium-$1$ and medium-$2$ respectively and $v_{2}$
And a plane wavefront $\mathrm{AB}$ propagating in the direction $\mathrm{AA}^{\prime}$ incident on the interface of two medium at an angle $i$.
Let $\tau$ be the time taken by the wavefront to travel the distance $\mathrm{BC}$.
$\therefore \mathrm{BC}=v_{1} \tau$
In order to determine the shape of the refracted wavefront, draw a sphere of radius $v_{2} \tau$ from the point $A$ in the second medium (the speed of the wave in the second medium is $v_{2}$ and the distance covered in time $\tau$ is $v_{2} \tau$.)
Let $\mathrm{CE}$ represent a tangent plane drawn from the point $\mathrm{C}$ on the sphere. Then $\mathrm{AE}=v_{2} \tau$ and $\mathrm{CE}$ would represent the refracted wavefront.
According to Huygen's principle of wavefront is as follow.
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The figure shows a surface $XY$ separating two transparent media, medium - $1$ and medium- $2$. The lines $ab$ and $cd$ represent wavefronts of a light wave traveling in medium- $1$ and incident on $XY$. The lines $ef$ and $gh$ represent wavefronts of the light wave in medium- $2$ after refraction.
The phases of the light wave at $c, d, e$ and $f$ are $\phi_c,\phi_d, \phi_e$ and $\phi_f$ respectively. It is given that $\phi_c \neq \phi_f.$
The figure shows a surface $XY$ separating two transparent media, medium - $1$ and medium- $2$. The lines $ab$ and $cd$ represent wavefronts of a light wave traveling in medium- $1$ and incident on $XY$. The lines $ef$ and $gh$ represent wavefronts of the light wave in medium- $2$ after refraction.
The phases of the light wave at $c, d, e$ and $f$ are $\phi_c,\phi_d, \phi_e$ and $\phi_f$ respectively. It is given that $\phi_c \neq \phi_f.$
Explain the reflection of a plane wave using Huygen's principle.
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A light beam is incident on a denser medium whose refractive index is $1.414$ at an angle of incidence $45^o$ . Find the ratio of width of refracted beam in a medium to the width of the incident beam in air
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- [NEET 2017]