Question

the refractive index of medium X with respect to medium Y is 2 by 3 the refractive index of medium with respect to medium Z is 4 by 3 find the refractive index of medium Z with respect to medium x if the speed of light in medium excess 3 into 10 power 8 metre per second. calculate the speed of light in medium Y.​

Answer 1

Explanation:

the refractive index of medium x is equal to 2 by 3 refractive index of medium Y is equal to 4 by 3 3 3 get cancelled 3 by 4 minutes of medium Z with respect to X

Answer 2

$\mu_{xz}=\frac{9}{8}$

$v_y=2\times 10^{8}\ m.s^{-1}$

Explanation:

refractive index of medium X with respect to Y, $\mu_{yx}=\frac{2}{3}$

refractive index of medium Y with respect to Z, $\mu_{zy}=\frac{4}{3}$

As we know that the refractive index of medium X with respect to Y can be given as the ratio of speed of light in medium Y to the speed of light in medium X.

Mathematically:

$\rm \mu_{yx}=\frac{speed\ of\ light\ in\ medium\ Y}{speed\ of\ light\ in\ medium\ X}=\frac{2}{3}$ .............................(1)

&  

$\rm \mu_{zy}=\frac{speed\ of\ light\ in\ medium\ Z}{speed\ of\ light\ in\ medium\ Y}=\frac{4}{3}$ ......................(2)

Now we need:

$\rm \mu_{xz}=\frac{speed\ of\ light\ in\ medium\ X}{speed\ of\ light\ in\ medium\ Z}$

From (1) & (2)

$\mu_{zx}=\mu_{yx}\times \mu_{zy}$

$\rm \mu_{zx}=\frac{v_y}{v_x}\times \frac{v_z}{v_y}$

where:

$v_x=$ velocity of light in medium x

$v_y=$ velocity of light in medium y

$v_z=$ velocity of light in medium z

So we have refractive index of medium X with respect to medium Z as:

$\mu_{zx}=\frac{2}{3}\times \frac{4}{3}$

$\mu_{zx}=\frac{8}{9}$

Now the refractive index of medium Z with respect to medium X will be:

$\mu_{xz}=\frac{1}{\mu_{zx}}$

$\mu_{xz}=\frac{9}{8}$

• Given that speed of light in medium X is, $v_x=3\times 10^8\ m.s^{-1}$

Now the speed of light in medium Y:

From (1)

$\mu_{yx}=\frac{2}{3}$

$\frac{v_y}{v_x}=\frac{2}{3}$

$v_y=\frac{2}{3}\times 3\times 10^8$

$v_y=2\times 10^{8}\ m.s^{-1}$

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TOPIC: refractive index

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