The index of refraction of water for a given monochromatic light in water is n=4/3. The wavelength of this light in water is 500nm.
a) find the speed of this light in water.
b) find the energy of one photon of this light .
Does this enerdy change if this light is propagated in vacuum? Justify
To find the answers to these questions, we can use the equation that relates the speed of light in a medium to its wavelength and the index of refraction:
v = c/n
Where:
- v is the speed of light in the medium,
- c is the speed of light in a vacuum, and
- n is the index of refraction of the medium.
Let's solve each question step by step:
a) Find the speed of this light in water.
To find the speed of light in water, we substitute the values into the equation:
v = c/n
Given that c is the speed of light in a vacuum (which is approximately 3 × 10^8 m/s) and n is the index of refraction of water (which is 4/3), we can calculate the speed of light in water:
v = (3 × 10^8 m/s) / (4/3)
= (3 × 10^8 m/s) * (3/4)
= 2.25 × 10^8 m/s
Therefore, the speed of light in water is approximately 2.25 × 10^8 m/s.
b) Find the energy of one photon of this light.
To find the energy of one photon of light, we can use the equation:
E = hf
Where:
- E is the energy of the photon,
- h is Planck's constant (approximately 6.63 × 10^-34 J·s), and
- f is the frequency of the light.
To find the frequency, we can use the formula:
f = c/λ
Where:
- f is the frequency of the light,
- c is the speed of light in a vacuum, and
- λ is the wavelength of the light.
Given that c is the speed of light in a vacuum (which is approximately 3 × 10^8 m/s) and λ is the wavelength of the light in water (which is 500 nm or 500 × 10^-9 m), we can calculate the frequency:
f = (3 × 10^8 m/s) / (500 × 10^-9 m)
= (3 × 10^8 m/s) * (2 × 10^9 / 1)
= 6 × 10^17 Hz
Now we can calculate the energy of one photon:
E = (6.63 × 10^-34 J·s) * (6 × 10^17 Hz)
= 39.78 × 10^-17 J
Therefore, the energy of one photon of this light is approximately 39.78 × 10^-17 J.
Does this energy change if this light is propagated in a vacuum?
No, the energy of one photon does not change if the light is propagated in a vacuum. The energy of a photon is determined solely by its frequency, which remains constant regardless of the medium the light is traveling through.