Q6E - University Physics with Modern Physics

Question

Light of a certain frequency has a wavelength of 526 nm in water. What is the wavelength of this light in benzene?

Step-by-Step Solution

Answer

The wavelength of light in benzene is 467 nm.

Step 1: Determination of the wavelength of light in benzene.

The expression for wavelength in any medium other than air is,

    $\lambda =\frac{{\lambda }_0}{n}$

Here, ${\lambda }_0$ is the wavelength in air and n is the refractive index.

Now,

  $$\begin{gathered} n_{water}=1.333 \\ {n}_{benzene}=1.501 \end{gathered}$$

Thus, solve for water and benzene,

$$\begin{gathered} {\lambda }_0={\lambda }_{water}{n}_{water} \\ {\lambda }_0={\lambda }_{benzene}{n}_{benzene} \end{gathered}$$

Equating both the equations,

$$\begin{gathered} {\lambda }_{benzene}={\lambda }_{water}\left(\frac{n_{water}}{n_{benzene}}\right) \\ =\left(526 nm\right)\left(\frac{1.333}{1.501}\right) \\ =467 nm \end{gathered}$$

Thus, the wavelength of light in benzene is 467 nm.