Light has a wavelength 600 nm in free space. it passes into the glass , which has an index of refraction of 1.50 what is the frequency of the light inside the glass?

Options

A. `3.3xx10^(14)Hz`
B. `5.0xx10^(14)Hz`
C. `3.3xx10^(5)Hz`
D. `5.0xx10^(5)Hz`

Answer

To find the frequency of light inside the glass, we can follow these steps:

### Step 1: Understand the relationship between speed, wavelength, and frequency
The speed of light in a medium can be expressed as:
\[ v = f \times \lambda \]
where:
- \( v \) is the speed of light in the medium,
- \( f \) is the frequency of the light,
- \( \lambda \) is the wavelength of the light.

### Step 2: Determine the speed of light in glass
The speed of light in a medium is related to the speed of light in vacuum (\( c \)) and the refractive index (\( n \)) of the medium:
\[ v = \frac{c}{n} \]
Given that the refractive index of glass is \( n = 1.50 \) and the speed of light in vacuum \( c \approx 3 \times 10^8 \, \text{m/s} \), we can calculate the speed of light in glass:
\[ v = \frac{3 \times 10^8 \, \text{m/s}}{1.50} = 2 \times 10^8 \, \text{m/s} \]

### Step 3: Convert the wavelength from nanometers to meters
The wavelength is given as \( 600 \, \text{nm} \). To convert this to meters:
\[ 600 \, \text{nm} = 600 \times 10^{-9} \, \text{m} = 6 \times 10^{-7} \, \text{m} \]

### Step 4: Calculate the frequency of light in glass
Now, we can use the speed of light in glass and the wavelength to find the frequency:
\[ f = \frac{v}{\lambda} \]
Substituting the values we have:
\[ f = \frac{2 \times 10^8 \, \text{m/s}}{6 \times 10^{-7} \, \text{m}} \]
Calculating this gives:
\[ f = \frac{2 \times 10^8}{6 \times 10^{-7}} = \frac{2}{6} \times 10^{8 + 7} = \frac{1}{3} \times 10^{15} \, \text{Hz} \]
Thus:
\[ f \approx 0.333 \times 10^{15} \, \text{Hz} \]

### Final Answer
The frequency of light inside the glass is approximately:
\[ f \approx 3.33 \times 10^{14} \, \text{Hz} \]