A ray of light is incident in medium $1$ on a surface that separates medium $1$ from medium $2$ . Let $v_{1}$ and $v_{2}$ represent the velocity of light in medium $1$ and medium $2$ respective. Also let $n_{12}$ and $n_{21}$ represent the refractive index of medium $1$ with respect to medium $2$ and refractive index of medium $2$ with respect to medium $1$ , respectively. If $i$ and $r$ denote the angle of incidence and refraction, then:

sin i / sin r = n_{21} = v_{1} / v_{2}

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sin i / sin r = n_{21} = v_{2} / v_{1}

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sin i / sin r = n_{12} = v_{1} / v_{2}

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sin i / sin r = n_{12} = v_{2} / v_{1}

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Solution

The correct option is A $sin i / sin r = n_{21} = v_{1} / v_{2}$
If $v_{1}$ and $v_{2}$ is velocity of light in medium 1 and medium 2 respective.

Then $n_{12}$ , the refractive index of medium 1 with respect to medium 2 is given by :
$n_{12} = \frac{v_{2}}{v_{1}} = \frac{1}{n_{21}}$

Now, according to Snell's law when light is incident on medium 1 with angle $i$ and refracts to medium 2 with angle $r$ then relation between them is given by:

$\frac{s i n i}{s i n r} = \frac{n_{2}}{n_{1}} = \frac{v_{1}}{v_{2}} = n_{21}$

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Similar questions

Q. A Ray of light is incident in medium one on a surface that separates medium one from medium to let V1 and V2 represent the velocity of light in medium one and medium to respective also let n12 and n21 respect the refractive index of medium one with respect to medium 2 and refractive index of medium two with respect to medium 1 respectively. if i and r denote the angles of incidence and refraction then
a)sin i/sin r=n12=v2/v1
b)sin i/sin r=n21=v2/v1
c)sin i/sin r=n12=v1/v2
d)sin i/sin r=n21=vi/v2

Q. If

v_{1}, v_{2}

and

c

represent the speed of light in medium

1

, medium

2

, and vacuum respectively, write the expression for
a)absolute refractive index of medium

1

b)absolute refractive index of medium

2

Hence show that,

η_{2} = \frac{v_{1}}{v_{2}}

How is refractive index of a medium 2 given with respect to medium 1 related to speed of light?
where, $n_{1}$ and $n_{2}$ are the respective refractive indicies of medium 1 and medium 2. And, $c_{1}$ and $c_{2}$ are speed of light in medium 1 and medium 2 respectively.