Question

Monochromatic light of wavelength 589nm is incident from air on a water surface. If $\mu $ for water is 1.33, find the wavelength, frequency and speed of the refracted light.

Answer 1

Note: We will first acknowledge all the values given to us in the question. Then we will simply apply the formula for the wavelength, frequency as well as the speed. Then we will solve it further. This will lead us to our desired answer. Refer to the solution below.
Formula used: $\lambda ' = \dfrac{\lambda }{\mu }$, $\upsilon = \dfrac{c}{\lambda }$, $v = \dfrac{c}{\mu }$.

Complete step-by-step solution -
Wavelength of the monochromatic light as per given in the question is- $\lambda = 589nm = 589 \times {10^{ - 9}}m$
The speed of light in vacuum is always considered to be- $c = 3 \times {10^8}m/s$
The refractive index of water as per given in the question is- $\mu = 1.33$
Let the wavelength of the refracted light be $\lambda '$.
Thus, the wavelength of the refracted light will be-
$ \Rightarrow \lambda ' = \dfrac{\lambda }{\mu } \\
   \Rightarrow \lambda ' = \dfrac{{589 \times {{10}^{ - 9}}}}{{1.33}} \\
   \Rightarrow \lambda ' = \dfrac{{589 \times {{10}^{ - 7}}}}{{133}} \\
   \Rightarrow \lambda ' = 4.42 \times {10^{ - 7}}m \\ $
Now, the frequency of the given monochromatic light will be-
$ \Rightarrow \upsilon = \dfrac{c}{\lambda } \\
   \Rightarrow \upsilon = \dfrac{{3 \times {{10}^8}}}{{589 \times {{10}^{ - 9}}}} \\
   \Rightarrow \upsilon = \dfrac{{3 \times {{10}^8} \times {{10}^9}}}{{589}} \\
   \Rightarrow \upsilon = 5.09 \times {10^{14}}Hz \\ $
The speed of the monochromatic light will be-
$ \Rightarrow v = \dfrac{c}{\mu } \\
   \Rightarrow v = \dfrac{{3 \times {{10}^8}}}{{1.33}} \\
   \Rightarrow v = \dfrac{{3 \times {{10}^{10}}}}{{133}} \\
   \Rightarrow v = 2.25 \times {10^8}m/s \\ $.

Note: Frequency, in physics, is the number of waves which go over a fixed point in unit time; also, the number of cycles or sensations felt by a body in periodic motion over one unit of time. A body is reported to have undergone one cycle or one vibration during periodical motion and return to its original state after a series of events or positions. See also angular speed; harmonic simple movement. The SI frequency scale is the hertz ( Hz), named after Heinrich Hertz, a German physicist. One hertz implies an incident is replicated once a second. If a television has a refresher rate of 1 inch the television will change (or refresh) the image once a second. Cycles per second (cps) is an earlier term for this unit. The second unit is the SI for the time.