A light of wavelength `6000 A` in air, enters a medium with refractive index 1.5 Inside the medium its frequency is….Hz and its wavelength is ….`A`

Explanation

To solve the problem, we need to find the frequency and wavelength of light when it enters a medium with a refractive index of 1.5.

### Step-by-Step Solution:

1. **Identify the given data**:
- Wavelength in air, \( \lambda_0 = 6000 \, \text{Å} = 6000 \times 10^{-10} \, \text{m} \)
- Refractive index of the medium, \( n = 1.5 \)

2. **Calculate the speed of light in air**:
- The speed of light in air (approximately) is \( c = 3 \times 10^8 \, \text{m/s} \).

3. **Calculate the frequency of light in air**:
- The frequency \( f \) can be calculated using the formula:
\[ f = \frac{c}{\lambda_0} \]
- Substituting the values:
\[ f = \frac{3 \times 10^8 \, \text{m/s}}{6000 \times 10^{-10} \, \text{m}} = \frac{3 \times 10^8}{6 \times 10^{-7}} = 5 \times 10^{14} \, \text{Hz} \]

4. **Calculate the speed of light in the medium**:
- The speed of light in the medium \( v \) is given by:
\[ v = \frac{c}{n} \]
- Substituting the values:
\[ v = \frac{3 \times 10^8 \, \text{m/s}}{1.5} = 2 \times 10^8 \, \text{m/s} \]

5. **Calculate the wavelength in the medium**:
- The wavelength \( \lambda \) in the medium can be calculated using the formula:
\[ \lambda = \frac{v}{f} \]
- Substituting the values:
\[ \lambda = \frac{2 \times 10^8 \, \text{m/s}}{5 \times 10^{14} \, \text{Hz}} = 4 \times 10^{-7} \, \text{m} = 4000 \, \text{Å} \]

### Final Answers:
- Frequency in the medium: \( 5 \times 10^{14} \, \text{Hz} \)
- Wavelength in the medium: \( 4000 \, \text{Å} \)