A soap bubble of index of refraction 1.43 strongly reflects both the red and the green components of white light. What minimum film thickness allows this to happen? (In air,the wavelength of red light is 703 nm, of green light 502.143 nm.)
Answer in units of nm
To find the minimum film thickness that allows for strong reflection of both the red and green components of white light, we can use the concept of optical path difference.
The condition for constructive interference in thin films can be expressed as:
2nt = mλ
Where:
- n is the refractive index of the film (in this case, the soap bubble)
- t is the thickness of the film
- m is the order of the interference (in this case, we are interested in the first order, so m = 1)
- λ is the wavelength of the light
For the red light, we have:
2nt_red = mλ_red
Substituting the given values:
2n_red * t = 1 * 703 nm
Similarly, for the green light:
2n_green * t = 1 * 502.143 nm
Since both the red and green interference paths must be equal, we can set them equal to each other:
2n_red * t = 2n_green * t
Simplifying, we have:
n_red * t = n_green * t
Dividing both sides by t:
n_red = n_green
So, the refractive index of the red light and the green light in the soap bubble must be equal for strong reflection to occur.
Now we can solve for the minimum film thickness t:
n_red = n_green = 1.43 (given)
From this equation:
1.43 * t = 1.43 * t
The thickness t cancels out, so we are left with:
1 = 1
This means that any thickness of the film will satisfy the condition for strong reflection of both red and green light. There is no minimum film thickness required in this case.
Therefore, the answer to the question is that there is no specific minimum film thickness mentioned in the given information.