the average speed of light slows to .75 c when it refracts through a particular peice of plastic.
a) What change is there in the light's frequency in the plastic?
b) It's wavelength?
To answer these questions, we need to know the relationship between the speed, frequency, and wavelength of light, which is given by the equation:
c = f * λ
Where:
- c is the speed of light in a vacuum (approximately 3 x 10^8 m/s),
- f is the frequency of light (measured in hertz, Hz),
- λ is the wavelength of light (measured in meters, m).
a) To find the change in frequency when light passes through the plastic, we can use the formula:
f' = f / n
Where:
- f' is the new frequency of light in the plastic,
- f is the original frequency of light,
- n is the refractive index of the plastic.
Given that the average speed of light slows to 0.75c in the plastic, the refractive index (n) can be calculated using the formula:
n = c / v
Where:
- c is the speed of light in a vacuum (approximately 3 x 10^8 m/s),
- v is the speed of light in the plastic (0.75c).
Let's calculate the refractive index (n) first:
n = c / v = (3 x 10^8 m/s) / (0.75c) = 4
Now we can find the new frequency (f'):
f' = f / n = (original frequency) / 4
b) To find the change in wavelength, we can use the formula:
λ' = λ * n
Where:
- λ' is the new wavelength of light in the plastic,
- λ is the original wavelength of light,
- n is the refractive index of the plastic.
Let's calculate the new wavelength (λ'):
λ' = λ * n = (original wavelength) * 4
By plugging in the values for the original frequency or wavelength, you can calculate the respective change in frequency or wavelength when light passes through the plastic.