What is the frequency of visible light with a wavelength of 500nm
The Correct Answer and Explanation is:
The frequency (( f )) of visible light with a wavelength (( \lambda )) of 500 nm can be calculated using the equation:
[
f = \frac{c}{\lambda}
]
where:
- ( f ) is the frequency of the light,
- ( c ) is the speed of light in a vacuum, approximately ( 3.00 \times 10^8 \, \text{m/s} ),
- ( \lambda ) is the wavelength in meters.
Given that the wavelength of light is 500 nm, we first need to convert nanometers to meters:
[
500 \, \text{nm} = 500 \times 10^{-9} \, \text{m} = 5.00 \times 10^{-7} \, \text{m}
]
Now we can use the formula to find the frequency:
[
f = \frac{3.00 \times 10^8 \, \text{m/s}}{5.00 \times 10^{-7} \, \text{m}}
]
Performing the division:
[
f = 6.00 \times 10^{14} \, \text{Hz}
]
So, the frequency of light with a wavelength of 500 nm is ( 6.00 \times 10^{14} \, \text{Hz} ).
Explanation:
Visible light is a part of the electromagnetic spectrum and consists of waves with varying wavelengths and frequencies. The wavelength of light determines its color, with visible wavelengths ranging from approximately 400 nm (violet) to 700 nm (red). The speed of light (( c )) is constant in a vacuum, meaning there is an inverse relationship between wavelength and frequency. As wavelength increases, frequency decreases, and vice versa.
In this case, the wavelength is 500 nm, which falls within the green portion of the visible spectrum. To find the frequency of this light, we apply the formula ( f = \frac{c}{\lambda} ), where ( c ) is the constant speed of light, and ( \lambda ) is the wavelength. After converting the wavelength to meters, we divide the speed of light by the wavelength, yielding a frequency of ( 6.00 \times 10^{14} \, \text{Hz} ).
This high frequency is typical of visible light, as electromagnetic waves in the visible range oscillate extremely quickly. Frequencies in this range interact with the human eye to produce the sensation of vision, and the specific frequency calculated corresponds to green light.