# The speed of light in air is $3 × 10^8\ m/s$. In medium X its speed is $2 × 10^8\ m/s$ and in medium Y the speed of light is $2.5 × 10^8\ m/s$. Calculate:(a) $_{air} \mathrm{n}_X$(b) $_{air} \mathrm{n}_Y$(c) $_{x} \mathrm{n}_Y$

Given:

Speed of light in air = $3 × 10^8\ m/s$.

Speed of light in medium X = $2 × 10^8\ m/s$

Speed of light in medium Y = $2.5 × 10^8\ m/s$

(a) To find: $_{air}\ {n}_{X}$

Solution:

$_{air}\ {n}_{X}=\frac {Speed\ of\ light\ in\ air}{Speed\ of\ light\ in\ medium\ X}$

$_{air}\ {n}_{X}=\frac {3 × 10^8\ m/s}{2 × 10^8\ m/s}$

$_{air}\ {n}_{X}=1.5$

(b) To find: $_{air}\ {n}_{Y}$

Solution:

$_{air}\ {n}_{Y}=\frac {Speed\ of\ light\ in\ air}{Speed\ of\ light\ in\ medium\ Y}$

$_{air}\ {n}_{Y}=\frac {3 × 10^8\ m/s}{2.5 × 10^8\ m/s}$

$_{air}\ {n}_{Y}=1.2$

(c) To find: $_{X}\ {n}_{Y}$

Solution:

$_{X}\ {n}_{Y}=\frac {Speed\ of\ light\ in\ medium\ X}{Speed\ of\ light\ in\ medium\ Y}$

$_{X}\ {n}_{Y}=\frac {2 × 10^8\ m/s}{2.5 × 10^8\ m/s}$

$_{X}\ {n}_{Y}=0.8$

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Updated on: 10-Oct-2022

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