Question

A monochromatic light of wavelength 589 nm is incident from air onto watersurface such that the refractive index of water is 1.33.

What is the wavelength and frequency of reflected light?

• A. $5890nm$
• B. $5\times {10}^{14}nm$
• C. $1.7nm$
• D. $589nm$

Answer 1

The correct option is D $589nm$

We know that, the frequency always remains the same during reflection and refraction.

The frequency of the incident light is $f=\frac{c}{\lambda }$

and $c_{\text{air}}=3\times {10}^8{\text{m s}}^{-1}$ and ${\lambda }_{\text{air}}=589\text{nm}$

Thus, $f_{\text{air}}=\frac{c_{\text{air}}}{{\lambda }_{\text{air}}}=\frac{3\times {10}^8}{589\times {10}^{-9}}\approx 5.1\times {10}^{14}\text{Hz}$

As the frequency doesn't change in reflection and refraction, $f_{\text{reflected}}=5.1\times {10}^{14}\text{Hz}$

And, in reflection, the light comes back to the same medium. Thus, wavelength of light remains same i.e., ${\lambda }_{\text{reflected}}=589\text{nm}$