Light of certain colour has 2000 waves per millimetre in air . What will be the wavelength of this light in a medium of refractive index 1.25 ?

Options

A. 1000 Å
B. 2000 Å
C. 3000 Å
D. 4000 Å

Explanation

To solve the problem, we need to find the wavelength of light in a medium with a refractive index of 1.25, given that there are 2000 waves per millimeter in air.

### Step-by-Step Solution:

1. **Understanding the Given Information**:
- We know that there are 2000 waves in 1 millimeter. This means that the wavelength (λ) can be calculated using the formula:
\[ \text{Wavelength} (\lambda) = \frac{\text{Distance}}{\text{Number of Waves}} \]
- Here, the distance is 1 millimeter (1 mm = \(10^{-3}\) meters) and the number of waves is 2000.

2. **Calculating the Wavelength in Air**:
- Using the formula:
\[ \lambda = \frac{1 \text{ mm}}{2000} = \frac{10^{-3} \text{ m}}{2000} \]
- Performing the division:
\[ \lambda = \frac{10^{-3}}{2000} = 5 \times 10^{-7} \text{ m} = 5000 \text{ angstroms} \quad (\text{since } 1 \text{ angstrom} = 10^{-10} \text{ m}) \]

3. **Using the Refractive Index to Find Wavelength in the Medium**:
- The relationship between the wavelength in air (or vacuum) and in a medium is given by:
\[ \lambda_m = \frac{\lambda}{n} \]
- Where \(n\) is the refractive index of the medium. Here, \(n = 1.25\).

4. **Calculating the Wavelength in the Medium**:
- Substituting the values we have:
\[ \lambda_m = \frac{5000 \text{ angstroms}}{1.25} \]
- Performing the division:
\[ \lambda_m = 4000 \text{ angstroms} \]

5. **Final Answer**:
- The wavelength of the light in the medium with a refractive index of 1.25 is **4000 angstroms**.