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The speed of light in vacuum and in two different glasses is given in the table below:
| Medium | Speed of Light |
| Vacuum | $3.00\times {10^8}m/s$ |
| Flint Glass | $1.86\times {10^8}m/s$ |
| Crown Glass | $1.97\times {10^8}m/s$ |
Given:
Medium = Vacuum
Speed of light in vacuum = $3.00\times {10^8}m/s$
Speed of light in flint glass = $1.86\times {10^8}m/s$
Speed of light in crown glass = $1.97\times {10^8}m/s$
(a) To find: Absolute refractive indexes of flint glass $(_{vacuum}\ {n}_{flint})$ and crown glass $(_{vacuum}\ {n}_{crown})$.
Solution:
From the formula of refractive index, we know that:
$Refractive\ index\ of\ a\ medium=\frac{Speed\ of\ light\ in\ medium\ 1}{Speed\ of\ light\ in\ medium\ 2}$
Therefore, here
$_{vacuum}\ {n}_{flint}=\frac {Speed\ of\ light\ in\ vacuum}{Speed\ of\ light\ in\ flint\ glass}$
Substituting the given values we get-
$_{vacuum}\ {n}_{flint}=\frac{3\times 10^{8} m/s}{1.86\times 10^{8} m/s}$
$_{vacuum}\ {n}_{flint}=1.61$
Thus, the absolute refractive index of flint glass is 1.61.
$_{vacuum}\ {n}_{crown}=\frac {Speed\ of\ light\ in\ vacuum}{Speed\ of\ light\ in\ crown\ glass}$
Substituting the given values we get-
$_{vacuum}\ {n}_{crown}=\frac{3\times 10^{8} m/s}{1.97\times 10^{8} m/s}$
$_{vacuum}\ {n}_{crown}=1.52$
Thus, the absolute refractive index of crown glass is 1.52.
(b) To find: Relative refractive index for light going from crown glass to flint glass $(_{crown}\ {n}_{flint})$.
Solution:
$_{crown}\ {n}_{flint}=\frac {Speed\ of\ light\ in\ crown\ glass}{Speed\ of\ light\ in\ flint\ glass}$
Substituting the given values we get-
$_{crown}\ {n}_{flint}=\frac {1.97\times 10^{8} m/s}{1.86\times 10^{8} m/s}$
$_{crown}\ {n}_{flint}=1.059$
Thus, the relative refractive index for light going from crown glass to flint glass is 1.059.
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