the average speed of light slows to 0.75 when it refracts through a praticular piece of plastic.
a. what change is there in the light's frequecny in the plastic?
b. in its wavelength?
You must mean that the speed of light slows to 0.75c in the plastic, not 0.75
a) frequency does not change
b) wavelength is shortened to 0.75 times the original wavelength (in air).
a. To determine the change in frequency, we can use Snell's Law, which says that the ratio of the speeds of light in two different media is equal to the ratio of the wavelengths in those media:
n₁ * λ₁ = n₂ * λ₂
where n₁ and n₂ are the refractive indices of the initial medium (air or vacuum) and the plastic, respectively, and λ₁ and λ₂ are the corresponding wavelengths.
Since we know that the speed of light in the plastic is 0.75 times its speed in air or vacuum, we can rewrite the equation as:
1 * λ₁ = 0.75 * λ₂
Dividing both sides of the equation by λ₂, we get:
1/λ₂ = 0.75/λ₁
So, the frequency of light remains the same when it refracts through the plastic.
b. Now, let's determine the change in wavelength. We can use the equation derived above:
1/λ₂ = 0.75/λ₁
Rearranging the equation to solve for λ₂, we get:
λ₂ = λ₁ / 0.75
Therefore, the wavelength of light in the plastic is 1/0.75 times the wavelength in the initial medium (air or vacuum).
To determine the change in frequency and wavelength of light when it passes through a particular piece of plastic, we need to use the relationship between speed, frequency, and wavelength.
a. Change in Frequency:
The speed of light in a vacuum is approximately 3 x 10^8 meters per second (m/s). When light passes through a medium like plastic, it slows down, resulting in a change in its frequency. The relationship between speed, frequency, and wavelength of light is given by the equation:
speed = frequency x wavelength
Since we want to find the change in frequency, we can rearrange the equation:
frequency = speed / wavelength
Given that the average speed of light in the plastic is 0.75 times its speed in a vacuum, the equation becomes:
0.75 x speed in vacuum = frequency in plastic x wavelength in plastic
Dividing both sides of the equation by the wavelength in plastic:
0.75 x speed in vacuum / wavelength in plastic = frequency in plastic
b. Change in Wavelength:
Similar to determining the change in frequency, we can rearrange the equation to find the change in wavelength:
wavelength = speed / frequency
Using the same equation as before and dividing both sides by the frequency in plastic:
0.75 x speed in vacuum / frequency in plastic = wavelength in plastic
By solving these equations, you can find the change in frequency and wavelength of light when it refracts through the particular piece of plastic.