What is the ratio of the wavelength of visible light of wavelength600 nm to that of an FM radio wave of frequency 100 MHz? c = 2.998x 108 m/s

L1 = 600 nm = 600*10-9 m = 6*10^-7 m.

L2 = V/F = 2.998*10^8/1*10^8 = 2.998 m.

L1/L2 = 6*10^-7m/2.998m = 2.001*10^-7.

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To find the ratio of the wavelength of visible light to that of an FM radio wave, we need to use the formula:

c = λ * f

where
c is the speed of light (2.998 x 10^8 m/s),
λ is the wavelength, and
f is the frequency.

For visible light with a wavelength of 600 nm (600 x 10^-9 m), we can calculate the frequency using the formula:

f = c / λ

f = (2.998 x 10^8 m/s) / (600 x 10^-9 m)
f = 4.997 x 10^14 Hz

Now, let's find the wavelength of the FM radio wave with a frequency of 100 MHz (100 x 10^6 Hz):

λ = c / f

λ = (2.998 x 10^8 m/s) / (100 x 10^6 Hz)
λ = 2.998 m

Finally, we can calculate the ratio of the two wavelengths:

Ratio = λ(visible light) / λ(FM radio wave)
Ratio = (600 x 10^-9 m) / (2.998 m)
Ratio = 2.001 x 10^-7

Therefore, the ratio of the wavelength of visible light of 600 nm to that of an FM radio wave of 100 MHz is approximately 2.001 x 10^-7.

To find the ratio of the wavelength of visible light (600 nm) to that of an FM radio wave (frequency = 100 MHz), you need to convert the wavelength of visible light to meters and then use the formula relating wavelength and frequency.

1. Convert the wavelength of visible light from nanometers (nm) to meters (m):
- Given: wavelength of visible light = 600 nm
- Conversion: 1 nm = 1 x 10^(-9) m
- Convert: wavelength of visible light = 600 nm x (1 x 10^(-9) m / 1 nm)
= 600 x 10^(-9) m
= 6 x 10^(-7) m

Therefore, the wavelength of visible light is 6 x 10^(-7) m.

2. Use the formula: speed of light (c) = wavelength (λ) x frequency (f)
Rearrange the formula to solve for wavelength (λ):
λ = c / f

Where:
- c is the speed of light (c = 2.998 x 10^8 m/s)
- f is the frequency

Given: frequency of the FM radio wave = 100 MHz
Convert the frequency to Hz:
1 MHz = 1 x 10^6 Hz
100 MHz = 100 x 10^6 Hz

3. Substitute the values into the formula:
λ = c / f
λ = 2.998 x 10^8 m/s / 100 x 10^6 Hz
λ = 2.998 x 10^2 m

Therefore, the wavelength of the FM radio wave is 2.998 x 10^2 m.

4. Finally, calculate the ratio between the two wavelengths:
Ratio = (wavelength of visible light) / (wavelength of FM radio wave)
= (6 x 10^(-7) m) / (2.998 x 10^2 m)
≈ 2 x 10^(-9)

Therefore, the ratio is approximately 2 x 10^(-9).