Approximate thickness of oil film to observe interference of light (due to which it looks coloured) is

Options

A. 10 mm
B. `10^-3 mm`
C. 10 cm
D. 1 cm

Answer

To determine the approximate thickness of an oil film required to observe interference of light that results in a colorful appearance, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Interference in Thin Films**:
- Interference occurs when light waves reflect off the two surfaces of a thin film (in this case, an oil film). The light waves can interfere constructively or destructively, leading to the colorful patterns observed.

2. **Path Difference**:
- For constructive interference (which produces bright colors), the path difference between the light waves reflecting off the top and bottom surfaces of the film must be an integer multiple of the wavelength of light. The condition for constructive interference is given by:
\[ 2t = m\lambda \]
where \( t \) is the thickness of the film, \( m \) is an integer (0, 1, 2,...), and \( \lambda \) is the wavelength of light.

3. **Minimum Thickness Calculation**:
- To find the minimum thickness \( t \) for the first order of interference (m=1), we can rearrange the equation:
\[ t = \frac{m\lambda}{2} \]
- For visible light, the average wavelength \( \lambda \) is approximately \( 5000 \) angstroms (or \( 5000 \times 10^{-10} \) meters).

4. **Substituting Values**:
- Substituting \( m = 1 \) and \( \lambda = 5000 \) angstroms into the equation gives:
\[ t = \frac{1 \times 5000 \times 10^{-10}}{2} = 2500 \times 10^{-10} \text{ meters} \]
- This can also be expressed in angstroms:
\[ t = 2500 \text{ angstroms} \]

5. **Final Conversion**:
- To convert angstroms to millimeters, we know that \( 1 \text{ angstrom} = 10^{-10} \text{ meters} \). Therefore:
\[ t = 2500 \times 10^{-10} \text{ meters} = 2.5 \times 10^{-7} \text{ meters} = 0.25 \times 10^{-3} \text{ millimeters} = 0.00025 \text{ millimeters} \]

6. **Conclusion**:
- The approximate thickness of the oil film required to observe interference of light is about \( 2500 \) angstroms or \( 0.25 \) micrometers.

### Final Answer:
The approximate thickness of the oil film to observe interference of light is \( 2500 \) angstroms.

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