A thin film of thickness `t` and index of refractive `1.33` coats a glass with index of refraction `1.50`.What is the least thickness `t` that will strong reflect light with wavelength `600nm` incident normally?

Options

A. 200 nm
B. 100 nm
C. 400 nm
D. 300 nm

Answer

To solve the problem of finding the least thickness \( t \) of a thin film that will strongly reflect light of wavelength \( 600 \, \text{nm} \) when incident normally, we can follow these steps:

### Step-by-Step Solution

1. **Identify the Given Values:**
- Wavelength of light, \( \lambda = 600 \, \text{nm} = 600 \times 10^{-9} \, \text{m} \)
- Refractive index of the thin film, \( \mu = 1.33 \)
- Refractive index of the glass, \( n = 1.50 \)

2. **Understand the Condition for Constructive Interference:**
For constructive interference in thin films, the condition is given by:
\[ 2 \mu t = n \lambda \]
where \( n \) is an integer (1, 2, 3, ...), \( t \) is the thickness of the film, and \( \lambda \) is the wavelength of light in vacuum.

3. **Rearranging the Formula to Find Thickness \( t \):**
We can rearrange the formula to solve for \( t \):
\[ t = \frac{n \lambda}{2 \mu} \]

4. **Substituting the Values:**
To find the least thickness, we take \( n = 1 \):
\[ t = \frac{1 \times 600 \times 10^{-9}}{2 \times 1.33} \]

5. **Calculating the Denominator:**
Calculate \( 2 \mu \):
\[ 2 \times 1.33 = 2.66 \]

6. **Final Calculation of Thickness \( t \):**
Now substitute back into the equation:
\[ t = \frac{600 \times 10^{-9}}{2.66} \]
Performing the division:
\[ t \approx 225.56 \times 10^{-9} \, \text{m} = 225.56 \, \text{nm} \]

Since we are looking for the least thickness, we round this to the nearest whole number:
\[ t \approx 226 \, \text{nm} \]

### Conclusion
The least thickness \( t \) that will strongly reflect light with a wavelength of \( 600 \, \text{nm} \) is approximately \( 226 \, \text{nm} \).