Question

The speed of a light wave in a certain transparent material is 0.683 times its speed in vacuum, which is 3.00 x 108 m/s. When yellow light with a frequency of 5.25 x 1014 Hz passes through this material, what is its wavelength in nanometers? wavelength: nm

Answer 1

Speed of light in medium V= 0.683 C = 0.683 x C3x18) = 2.048 x108 mis wandength is given by 1- ^ - 2.043x10* mis 5.25 x 104 Hz LO = 0.390 x10-6 m = 390x109 m. = 390 nm .nm

390 nm

Answer 2

The wave speed ?$v$ is

$$v=\varphi c$$

where ?$\varphi$ is the given factor and ?$c$ denotes the speed of light in vacuum, which is 3.00×108 m/s$3.00\times {10}^8\text{ m/s}$.

For all periodic waves, the wave speed ?$v$, frequency ?$f$, and wavelength ?$\lambda$ are related by

$$f\lambda =v$$

Solve for ?$\lambda$ and substitute the expression for the wave speed in terms of the speed of light in vacuum. This gives the requested wavelength in terms of given quantities.

$$\lambda =\frac{v}{f}=\frac{\varphi c}{f}$$

To obtain the numerical answer, substitute the data and convert the result to nanometers as requested.

?=0.583(3.00×108 m/s)(5.23×1014 Hz)=3.34×10−7 m=334 nm