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Question

Why to is said that frequency of light remain same in all media

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Solution

Think of a pond. Let's say I create waves somewhere in that pond with my hand or maybe a paddle. I create exactly one wave per second, or 3600 waves every hour. At the end of the day, I'll have created 86,400 waves.

These waves travel across the pond. Depending on the depth of the water, depending on the vegetation, etc., the waves travel at different speed. But at the end of the day, you'll count exactly the same 86,400 waves that I created. Otherwise, unless the waves coalesce or split, there'd be either a deficit or a surplus of waves somewhere... and it would be a deficit or surplus that will grow to infinity since we are under no obligation to stop this little experiment after just one day.

The same thing happens with the electromagnetic field. A frequency f means that the electromagnetic field is yanked back-and-forth by something charged f times a second. So f waves are created each second. Again, unless waves coalesce or split (that would take us to the realm of nonlinear optics) f waves a second at one end of the pond means f waves a second at the other end as otherwise, there'd be an ever growing surplus or deficit of waves.

Meanwhile, the distance between waves (that is, the wavelength) can change, to account for the varying speed of travel through different mediums.


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