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 pm`
D. 1 cm

Answer

To find the approximate thickness of an oil film required to observe interference of light, we need to consider the wavelength of visible light and how it relates to the thickness of the film.

### Step-by-Step Solution:

1. **Understanding the Concept of Interference**:
- Interference of light occurs when light waves overlap and combine, leading to a pattern of bright and dark fringes. For this to happen, the thickness of the film must be comparable to the wavelength of visible light.

2. **Identifying the Wavelength Range**:
- The wavelength of visible light ranges from approximately 4000 Å (angstroms) to 8000 Å.
- In meters, this range is:
- 4000 Å = 4000 × 10^-10 m = 4 × 10^-7 m
- 8000 Å = 8000 × 10^-10 m = 8 × 10^-7 m

3. **Converting Wavelength to Millimeters**:
- To convert the wavelengths from meters to millimeters:
- 1 meter = 1000 millimeters
- Therefore,
- 4000 Å = 4 × 10^-7 m = 4 × 10^-4 mm
- 8000 Å = 8 × 10^-7 m = 8 × 10^-4 mm

4. **Determining the Approximate Thickness**:
- The thickness of the oil film should be on the order of the wavelength of visible light, which is approximately between 4 × 10^-4 mm and 8 × 10^-4 mm.
- Thus, the approximate thickness of the oil film is around 8 × 10^-4 mm.

5. **Choosing the Closest Option**:
- Now, we compare our calculated thickness with the given options:
- Option 1: 10 mm
- Option 2: 10^-3 mm (which is 0.001 mm)
- Option 3: ±10 (not a valid thickness)
- Option 4: 1 cm (which is 10 mm)
- The closest value to 8 × 10^-4 mm is Option 2: 10^-3 mm.

### Conclusion:
The approximate thickness of the oil film to observe interference of light is best represented by **Option 2: 10^-3 mm**.