Blue light of wavelength 480 nm is most strongly reflected off a thin film of oil on a glass slab when viewed near normal incidence. Assuming that the index of refraction of the oil is 1.2 and that of the glass is 1.6, what is the minimum thickness of the oil film (other then zero)?

Options

A. 100 nm
B. 200 nm
C. 300 nm
D. none

Explanation

To solve the problem of finding the minimum thickness of the oil film that causes blue light (wavelength 480 nm) to be most strongly reflected, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Setup**: We have a thin film of oil on a glass slab, with air above the oil. The indices of refraction are given as:
- \( n_{\text{oil}} = 1.2 \)
- \( n_{\text{glass}} = 1.6 \)
- \( n_{\text{air}} \approx 1.0 \)

2. **Condition for Strong Reflection**: For constructive interference (strong reflection) in thin films, the condition is given by:
\[ 2 \mu t = n \lambda \]
where:
- \( \mu \) is the refractive index of the film (oil in this case),
- \( t \) is the thickness of the film,
- \( n \) is the order of interference (for minimum thickness, we take \( n = 1 \)),
- \( \lambda \) is the wavelength of light in vacuum (or air).

3. **Wavelength in the Oil**: The wavelength of light in the oil can be calculated using the formula:
\[ \lambda_{\text{oil}} = \frac{\lambda_{\text{air}}}{n_{\text{oil}}} \]
where \( \lambda_{\text{air}} = 480 \, \text{nm} \). Thus,
\[ \lambda_{\text{oil}} = \frac{480 \, \text{nm}}{1.2} = 400 \, \text{nm} \]

4. **Substituting Values**: Now, substituting the values into the interference condition for the minimum thickness:
\[ 2 \mu t = n \lambda \]
becomes:
\[ 2 \times 1.2 \times t = 1 \times 400 \, \text{nm} \]
Simplifying this gives:
\[ 2.4t = 400 \, \text{nm} \]

5. **Solving for Thickness \( t \)**:
\[ t = \frac{400 \, \text{nm}}{2.4} \approx 166.67 \, \text{nm} \]

6. **Final Answer**: The minimum thickness of the oil film (other than zero) is approximately \( 166.67 \, \text{nm} \).

### Summary of the Calculation:
- The minimum thickness \( t \) for strong reflection is calculated using the formula \( t = \frac{n \lambda}{2 \mu} \).
- Substituting \( n = 1 \), \( \lambda = 400 \, \text{nm} \), and \( \mu = 1.2 \) gives \( t \approx 166.67 \, \text{nm} \).