The human eye is most sensitive to light having a frequency of about 5.3*10^14 Hz, which is in the yellow-green region of the electromagnetic spectrum. How many wavelengths of this light can fit across the width of your thumb, a distance of about 2.0 cm?
First you need to calculate the wavelength L of that frequency of light, using the formula
L = (speed of light)/frequency
Use c = 3.00*10^10 cm/s for the speed of light
L = (3.00 cm/s)/(5.3*10^14 s^-1)= 5.66*10^-5 cm
Divide your thumb's width by that wavelength to get the number of waves.
Speed of light is 3x10^8 m/s and wavelength is 5.3*10^14, so you can use the equation
v=lambda(frequency) to find the frequency, and use the speed of light for your velocity.
Then just divide the width on your thumb by the wavelength
Well, let me give you a hand with that! The wavelength of light in the yellow-green region is about 5.7 x 10^-7 meters. Now, to figure out how many wavelengths can fit across your thumb, we'll divide the width of your thumb (2.0 cm or 0.02 meters) by the wavelength.
So, 0.02 meters / 5.7 x 10^-7 meters = a whopping number of wavelengths that would make your thumb wavy! It's approximately 3.5 x 10^7 wavelengths. Now that's a long thumb indeed!
To find the number of wavelengths of this light that can fit across the width of your thumb, we need to know the formula for calculating the number of wavelengths in a given distance.
The formula for calculating the number of wavelengths is:
Number of Wavelengths = Distance / Wavelength
We know that the human eye is most sensitive to light with a frequency of about 5.3*10^14 Hz. The speed of light in a vacuum is approximately 3.0*10^8 meters per second. To find the wavelength of this light, we can use the formula:
Wavelength = Speed of Light / Frequency
Substituting the values, we get:
Wavelength = (3.0*10^8 m/s) / (5.3*10^14 Hz)
Now we can calculate the wavelength:
Wavelength = 5.66*10^-7 meters
To find the number of wavelengths that can fit across the width of your thumb, which is approximately 2.0 cm or 0.02 meters, we can use the formula mentioned earlier:
Number of Wavelengths = Distance / Wavelength
Number of Wavelengths = 0.02 m / (5.66*10^-7 m)
Now we can calculate the number of wavelengths:
Number of Wavelengths ≈ 3.53*10^7
Therefore, approximately 35.3 million wavelengths of this light can fit across the width of your thumb.