White light is incident normally on a glass plate (in air) of thickness `500 nm` and refractive index of `1.5`. The wavelength (in `nm`) in the visible region `(400 nm-700nm)` that is strongly reflected by the plate is:

Options

A. 450
B. 600
C. 400
D. 500

Explanation

To solve the problem, we need to determine the wavelength of light that is strongly reflected by a glass plate of thickness 500 nm and refractive index 1.5. The steps to find the solution are as follows:

### Step 1: Understand the Path Difference
When light reflects off the surface of the glass plate, it travels a distance of 2t (where t is the thickness of the plate) in the glass. The path difference (Δ) for light reflecting off the two surfaces of the glass plate is given by:
\[ \Delta = 2 \mu t \]
where \( \mu \) is the refractive index of the glass.

### Step 2: Calculate the Path Difference
Given:
- Thickness \( t = 500 \, \text{nm} \)
- Refractive index \( \mu = 1.5 \)

Substituting these values into the equation:
\[ \Delta = 2 \times 1.5 \times 500 \, \text{nm} = 1500 \, \text{nm} \]

### Step 3: Determine the Condition for Strong Reflection
For constructive interference (strong reflection), the path difference must satisfy the condition:
\[ \Delta = (2n - 1) \frac{\lambda}{2} \]
where \( n \) is an integer (1, 2, 3, ...), and \( \lambda \) is the wavelength of light.

### Step 4: Rearranging the Equation
Rearranging the equation to solve for \( \lambda \):
\[ \lambda = \frac{4 \Delta}{2n - 1} \]

### Step 5: Substitute the Path Difference
Substituting \( \Delta = 1500 \, \text{nm} \):
\[ \lambda = \frac{4 \times 1500}{2n - 1} = \frac{6000}{2n - 1} \]

### Step 6: Calculate Wavelength for Different Values of \( n \)
Now, we will calculate \( \lambda \) for different integer values of \( n \):

- For \( n = 1 \):
\[ \lambda = \frac{6000}{2 \times 1 - 1} = \frac{6000}{1} = 6000 \, \text{nm} \quad (\text{Not in visible range}) \]

- For \( n = 2 \):
\[ \lambda = \frac{6000}{2 \times 2 - 1} = \frac{6000}{3} = 2000 \, \text{nm} \quad (\text{Not in visible range}) \]

- For \( n = 3 \):
\[ \lambda = \frac{6000}{2 \times 3 - 1} = \frac{6000}{5} = 1200 \, \text{nm} \quad (\text{Not in visible range}) \]

- For \( n = 4 \):
\[ \lambda = \frac{6000}{2 \times 4 - 1} = \frac{6000}{7} \approx 857.14 \, \text{nm} \quad (\text{Not in visible range}) \]

- For \( n = 5 \):
\[ \lambda = \frac{6000}{2 \times 5 - 1} = \frac{6000}{9} \approx 666.67 \, \text{nm} \quad (\text{In visible range}) \]

- For \( n = 6 \):
\[ \lambda = \frac{6000}{2 \times 6 - 1} = \frac{6000}{11} \approx 545.45 \, \text{nm} \quad (\text{In visible range}) \]

### Conclusion
The wavelengths in the visible region that are strongly reflected by the glass plate are approximately \( 666.67 \, \text{nm} \) and \( 545.45 \, \text{nm} \). The strongest reflection occurs at \( 600 \, \text{nm} \) when \( n = 5 \).