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Light travels with a speed of $2 \times 10^{8} \mathrm{~m} / \mathrm{s}$ in crown glass of refractive index $1.5$. What is the speed of light in dense flint glass of refractive index $1.8 ?$
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The correct answer is:
$1.67 \times 10^{8} \mathrm{~m} / \mathrm{s}$
We know that the refractive index of a medium is given by
$\mu=\frac{\mathrm{c}_{0}}{\mathrm{c}}$
Where $\mathrm{c}=$ velocity of light in the medium $\mathrm{c}_{\mathrm{o}}=$ velocity of light in vacuum For crown glass,
$1.5=\frac{\mathrm{c}_{\mathrm{o}}}{2 \times 10^{8}}$ ...(1)
For flint glass, $1.8=\frac{\mathrm{c}_{\mathrm{o}}}{\mathrm{c}}$ ...(2)
Dividing (2) by (1), we get $\frac{2 \times 10^{8}}{\mathrm{c}}=\frac{1.8}{1.5}$ or $\mathrm{c}=\frac{1.5 \times 2 \times 10^{8}}{1.8} \mathrm{~m} / \mathrm{s}=1.67 \times 10^{8} \mathrm{~m} / \mathrm{s}$
$\mu=\frac{\mathrm{c}_{0}}{\mathrm{c}}$
Where $\mathrm{c}=$ velocity of light in the medium $\mathrm{c}_{\mathrm{o}}=$ velocity of light in vacuum For crown glass,
$1.5=\frac{\mathrm{c}_{\mathrm{o}}}{2 \times 10^{8}}$ ...(1)
For flint glass, $1.8=\frac{\mathrm{c}_{\mathrm{o}}}{\mathrm{c}}$ ...(2)
Dividing (2) by (1), we get $\frac{2 \times 10^{8}}{\mathrm{c}}=\frac{1.8}{1.5}$ or $\mathrm{c}=\frac{1.5 \times 2 \times 10^{8}}{1.8} \mathrm{~m} / \mathrm{s}=1.67 \times 10^{8} \mathrm{~m} / \mathrm{s}$
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