The index of refraction of glass for violet light is 1.665 and for red light 1.618. Compute the difference in the speed of light in glass for the two colours.

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Solution

Given,
Refractive index for violet, $μ_{v} = 1.665$

Refractive index for red; $μ_{r} = 1.618$

We know,

$μ = \frac{c}{v}$

$v = \frac{c}{μ}$

$\Rightarrow$ $V_{v} = \frac{c}{μ_{v}} = \frac{3 \times 10^{8}}{1.665}$

$V_{r} = \frac{c}{μ_{r}} = \frac{3 \times 10^{8}}{1.665}$

Difference $= | V_{v} - V_{r} |$

$= ∣ ∣ ∣ \frac{3 \times 10^{8}}{1.665} - \frac{3 \times 10^{8}}{1.618} ∣ ∣ ∣ = 0.05 \times 10^{8}$

$Δ V = 5 \times 10^{6} m / s$

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The index of refraction of glass for violet light is 1.665 and for red light 1.618. Compute the difference in the speed of light in glass for the two colours.

Given, Refractive index for violet, μv=1.665Refractive index for red; μr=1.618We know,μ=cvv=cμ⇒ Vv=cμv=3×1081.665Vr=cμr=3×1081.665Difference =|Vv−Vr|=∣∣∣3×1081.665−3×1081.618∣∣∣=0.05×108ΔV=5×106m/s