Question

The speed of a light wave in a certain transparent material is 0.6310.631 times its speed in vacuum, which is 3.00×108 m/s3.00×108 m/s . When yellow light with a frequency of 5.15×1014 Hz 5.15×1014 Hz passes through this material, what is its wavelength in nanometers

Answer 1

367.57 nm

Step-by-step explanation:

Given that the speed of the light in certain material is 0.6310 times the speed of light in vacuum.

Speed of light in vacuum = 3×10⁸ m/s

Speed of the light in that material = 0.6310×3×10⁸ m/s = 1.893×10⁸ m/s

The frequency of the light does not change but the wavelength of the light changes with change in the speed when light travels from one medium to another.

Thus, frequency = 5.15×10¹⁴ Hz

Using,

c = frequency × Wavelength

Wavelength = c / frequency = (1.893×10⁸ m/s) / (5.15×10¹⁴ Hz) = 367.57×10⁻⁹ m

Also,

1 nm = 10⁻⁹ m

So, wavelength = 367.57 nm