The human eye is sensitive to electromagenetic waves that have wavelengths in the range from 400nm to 700nm (1nm=10^-9m). What range of the frequencies of electromagentic radiation can the eye detect?
Can you please show me the steps and work because i don't understand what i am supposed to do to solve.
The wave equation:
frequency*wavelength= speed of light
solve for frequency.
To find the range of frequencies of electromagnetic radiation that the human eye can detect, we need to use the wave equation:
frequency * wavelength = speed of light
We know that the speed of light is a constant value, which is approximately 3.00 * 10^8 meters per second (m/s). The wavelength range for the human eye is given as 400 nm to 700 nm. Let's plug in these values:
For the lower wavelength (400nm), we have:
frequency * 400 nm = 3.00 * 10^8 m/s
First, we need to convert the wavelength from nanometers (nm) to meters (m). Since 1 nm = 10^-9 m, we have:
frequency * 400 * 10^-9 m = 3.00 * 10^8 m/s
Simplifying, we get:
frequency = (3.00 * 10^8 m/s) / (400 * 10^-9 m)
Next, we can simplify the denominator by multiplying 400 by 10^-9:
frequency = (3.00 * 10^8 m/s) / (4 * 10^-7 m)
To divide by a fraction, we can multiply by its reciprocal:
frequency = (3.00 * 10^8 m/s) * (1 / (4 * 10^-7 m))
Multiplying the numerator and denominator, and simplifying, we get:
frequency = (3.00 * 10^8) / (4 * 10^-7) Hz
This can be further simplified by dividing the numerator and denominator by 4:
frequency = (0.75 * 10^8) / 10^-7 Hz
Using the rules of scientific notation, when dividing powers of 10, we subtract the exponents:
frequency = 0.75 * 10^15 Hz
Therefore, the lower frequency that the human eye can detect is approximately 0.75 * 10^15 Hz.
We can follow the same steps for the upper wavelength (700 nm), and find the upper frequency that the human eye can detect using the wave equation.
Do the calculation and you will find that the upper frequency that the human eye can detect is approximately 1.43 * 10^15 Hz.
Thus, the range of frequencies of electromagnetic radiation that the human eye can detect is approximately 0.75 * 10^15 Hz to 1.43 * 10^15 Hz.