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.
Similar Questions
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 $\phi_c \neq \phi_f.$
By Huygen's wave theory of light, we cannot explain the phenomenon of
By Huygen's wave theory of light, we cannot explain the phenomenon of
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
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
- [NEET 2017]
The idea of secondary wavelets for the propagation of a wave was first given by
The idea of secondary wavelets for the propagation of a wave was first given by
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 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 $3.$
- [IIT 2007]