if a monochromatic beam of light with a wavelength of 590 nanometers is traveling through air then enters a region of space where the index of refraction is 1.5, what will the light beam do? increase, decrease, or stay the same?
It slows down, shorter wavelength, same frequency
(note it can not change frequency. There is no storage of waves, the same number have to pass a given point per unit time on each side.)
lambda = V * T
so
lambda = V/f
if V goes down/ lambda goes down
To determine what will happen to the monochromatic beam of light with a wavelength of 590 nanometers when it enters a region of space with an index of refraction of 1.5, we need to understand the concept of refraction.
Refraction occurs when light passes from one medium to another, and the speed of light changes due to the change in the properties of the medium. The index of refraction (n) is a measure of how much the speed of light is decreased when it enters a particular medium compared to its speed in vacuum or air.
The formula to calculate the speed of light in a medium is: v = c/n, where v is the speed of light in the medium, c is the speed of light in vacuum or air, and n is the index of refraction of the medium.
In this case, the monochromatic beam of light is initially traveling through air, which has an index of refraction close to 1 (for simplicity). When it enters the region of space with an index of refraction of 1.5, the speed of light will decrease because the index of refraction is greater than 1.
From the formula above, we can see that if the value of n is greater than 1, the speed of light in the medium (v) will be smaller than the speed of light in vacuum or air (c), which means the light beam will decrease its speed when it enters the medium.
Now, let's determine how this change in speed impacts the wavelength of the light beam. The relationship between wavelength (λ), frequency (f), and the speed of light (v) is given by the formula: v = λf.
Since the frequency of the light beam remains constant, if the speed (v) decreases, the wavelength (λ) must also decrease to maintain the equation. Therefore, when the monochromatic beam of light enters the region of space with an index of refraction of 1.5, its wavelength will decrease as well.
In conclusion, when the monochromatic beam of light with a wavelength of 590 nanometers enters a region of space where the index of refraction is 1.5, the light beam will decrease in speed and its wavelength will also decrease.