A thin layer of liquid methylene iodide (n=1.756) is sandwiched between two flat parallel plates of glass (n=1.50). What must be the thickness of the liquid layer if normally incident light with in air is to be strongly reflected?((2m+1),85.4nm)
To determine the thickness of the liquid layer for strong reflection of normally incident light, we can make use of the concept of interference in thin films.
When light passes through the interface between two media with different refractive indices, part of the light is reflected and part is transmitted. The reflected light undergoes a phase change of 180 degrees.
For strong reflection, we need to ensure that the reflected waves from both the upper and lower surfaces of the liquid layer interfere constructively. This occurs when the path difference between the two reflected waves is an odd integer multiple of half the wavelength.
Here's how we can determine the thickness:
1. Calculate the wavelength of the incident light in the liquid medium:
Since the light is in air, we can use the formula: λ/λ₀ = n/n₀, where λ₀ is the incident light wavelength in air (85.4 nm) and n₀ is the refractive index of air (approximately 1).
λ/85.4 nm = n/1.50
λ = (n × 85.4 nm) / 1.50
2. Determine the path difference for interference:
The path difference between the two reflected waves is twice the thickness of the liquid layer, as the waves travel through the layer twice.
Path difference = 2 × thickness = 2d
3. Set up the interference condition:
The path difference should be an odd integer multiple of half the wavelength.
2d = (2m + 1) × (λ/2), where m is an integer representing the order of the interference (0, 1, 2, ...).
4. Solve for the thickness (d):
Divide both sides of the equation by 2:
d = (2m + 1) × (λ/4)
Substitute the value of λ from step 1.
Now you can calculate the thickness (d) by plugging in the values of the refractive indices and the wavelength, and choosing an appropriate order (m) to obtain the desired condition for strong reflection of light.