Question

Light waves are electromagnetic waves that travel at 3.00 108 m/s. The eye is most sensitive to light having a wavelength of 5.50 10-7 m. (a) Find the frequency of this light wave. Hz (b) Find its period. s

Answer 1

(a) $5.5\cdot 10^{14} Hz$

Explanation:

The relationship between wavelength, frequency and speed of an electromagnetic wave is:

$v=f \lambda$

where v is the speed, f is the frequency, $\lambda$ is the wavelength.

For the light wave in the problem, we have:

$v=3.00\cdot 10^8 m/s$ is the speed of light

$\lambda=5.50 \cdot 10^{-7} m$ is the wavelength

Substituting these numbers into the equation, and re-arranging it, we find the frequency of the light wave:

$f=\frac{v}{\lambda}=\frac{3\cdot 10^8 m/s}{5.5\cdot 10^{-7} m}=5.5\cdot 10^{14} Hz$

(b) $1.8\cdot 10^{-15} s$

Explanation:

The period of a wave is equal to the reciprocal of the frequency:

$T=\frac{1}{f}$

where f is the frequency of the wave, which we found in the previous part of the exercise. Substituting, we find:

$T=\frac{1}{f}=\frac{1}{5.5\cdot 10^{14} Hz}=1.8\cdot 10^{-15} s$