A parallel beam of light of wavelength 560 nm falls on a thin film of oil (refractive index = 1.4). What should be the minimum thickness of the film so that it strongly transmit the light ?

Explanation

To find the minimum thickness of the oil film that allows strong transmission of light, we can use the following steps:

### Step 1: Understand the Condition for Strong Transmission
For a thin film to strongly transmit light, we need to consider the interference of light waves. The condition for constructive interference (strong transmission) in a thin film with a refractive index greater than that of the surrounding medium is given by:
\[ 2nt = (m + \frac{1}{2})\lambda \]
where:
- \( n \) is the refractive index of the film,
- \( t \) is the thickness of the film,
- \( \lambda \) is the wavelength of light in vacuum,
- \( m \) is an integer (0, 1, 2,...).

### Step 2: Rearranging the Formula
To find the minimum thickness \( t \), we can rearrange the formula:
\[ t = \frac{(m + \frac{1}{2})\lambda}{2n} \]
For the minimum thickness, we set \( m = 0 \):
\[ t = \frac{\frac{1}{2}\lambda}{2n} = \frac{\lambda}{4n} \]

### Step 3: Substitute the Given Values
We are given:
- Wavelength \( \lambda = 560 \, \text{nm} = 560 \times 10^{-9} \, \text{m} \)
- Refractive index \( n = 1.4 \)

Now substituting these values into the equation:
\[ t = \frac{560 \times 10^{-9} \, \text{m}}{4 \times 1.4} \]

### Step 4: Calculate the Thickness
Calculating the denominator:
\[ 4 \times 1.4 = 5.6 \]

Now substituting back:
\[ t = \frac{560 \times 10^{-9}}{5.6} \]

Calculating the thickness:
\[ t = 100 \times 10^{-9} \, \text{m} = 100 \, \text{nm} \]

### Final Answer
The minimum thickness of the oil film for strong transmission of light is:
\[ t = 100 \, \text{nm} \]

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