The speed of light in air is very nearly the same as the speed of light in vacuu

Question

The speed of light in air is very nearly the same as the speed of light in vacuum, namely 3.0 x 108 m/s.

1) Monochromatic light emitted from a particular lamp has a wavelength of 630 nanometers. (The prefix "nano" means "one billionth", so 1 nanometer equals one billionth of a meter. In other words, 1 nm = 10-9 m.) What is the frequency of this light?

2) A monochromatic light source emits light with a frequency of 600 gigaHertz? (The prefix "giga" means "one billion", so 1 gigaHertz equals one billion Hz. In other words, 1 GHz = 109 Hz.) What is the wavelength of this light? Give your answer in both meters and nanometers.

3) A certain air defense installation for tracking airplanes uses transmits electromagnetic waves having a wavelngth of 6 cm. (This wavelength falls into the catagory of microwaves in the electromagnetic spectrum. What is the frequency of this radiation? Give your answer in both Hertz and gigaHertz.

Explanation / Answer

here,

Wavelength(w) = Speed of light(c) / frequency(f)

Part A:
w = 630 nm = 630*10^-9 m

f = c/w = 3*10^8/(630*10^-9)
f = 4.762*10^14 Hz

Part B:
f = 600 GHz = 6*10^11 Hz

w = c/f = 3*10^8/(6*10^11)
w = 0.0005 m

Since, 1m = 10^9 nm
w = 5*10^5 nm

Part C:
w = 6 cm = 0.06 m

f = 3*10^8/(0.06)
f = 5*10^9 Hz

1Hz = 10^-9 GHz

f = 5 GHz

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