Question

Bending Light The speed of yellow sodium light (wavelength, $589$nano-meters) in a certain liquid is measured to be $1.92\times {10}^8$meters per second. What is the index of refraction of this liquid, with respect to air, for sodium light?

[Hint: The speed of light in air is approximately $2.998\times {10}^8$meters per second.]

Short answer

The index of refraction of this liquid, with respect to air, for sodium light is$1.56$.

Step-by-step solution

Step 1. Given Information

The speed of yellow sodium light (wavelength,$589$nano-meters) in a certain liquid is measured to be $1.92\times {10}^8$meters per second.

We have to find the index of refraction of this liquid, with respect to air, for sodium light.

[Hint: The speed of light in air is approximately localid="1647102948259" $2.998\times {10}^8$meters per second.]

Step 2. The index of refraction is given as n=cv where c is speed of light in vaccum and v is speed of light in medium.

$c=2.998\times {10}^8\mathrm{and}v=1.92\times {10}^8$

Putting the value

$$\begin{gathered} n=\frac{2.998\times {10}^8}{1.92\times {10}^8} \\ n\approx 1.56 \end{gathered}$$

The index of refraction of this liquid, with respect to air, for sodium light is $1.56$.