91Ó°ÊÓ

To calculate the frequency of a light wave, you need to understand the relationship between speed, wavelength, and frequency. The formula to find the frequency (\( f \)) of light is:

• \( f = \frac{c}{\lambda} \)

Here, \( c \) is the speed of light in a vacuum or air, which is approximately \( 3 \times 10^8 \text{ m/s} \). \( \lambda \) is the wavelength of the light.
For yellow sodium light in air, the problem gives us \( \lambda_{\text{air}} = 589 \text{ nm} \), which can be converted to meters (\( 589 \times 10^{-9} \text{ m} \)).
By substituting these values into the formula, you can calculate the frequency:

• \( f = \frac{3 \times 10^8 \text{ m/s}}{589 \times 10^{-9} \text{ m}} \approx 5.09 \times 10^{14} \text{ Hz} \)

This frequency means the number of wave cycles that pass through a point each second is approximately \( 5.09 \times 10^{14} \). Understanding this relationship helps in knowing how light behaves when traveling through different mediums.

The index of refraction, denoted by \( n \), is a measure of how much the speed of light is reduced inside a medium compared to its speed in a vacuum. The index of refraction can be calculated using the formula:

• \( n = \frac{c}{v} \)

Here, \( c \) is the speed of light in a vacuum, and \( v \) is the speed of light in the medium.Another way to use the index is in calculating the wavelength in a different medium. In this exercise, the wavelength of yellow sodium light in glass can be found using:

• \( \lambda_{\text{glass}} = \frac{\lambda_{\text{air}}}{n} \)

For the given problem:

• \( n = 1.92 \)
• \( \lambda_{\text{glass}} = \frac{589 \times 10^{-9} \text{ m}}{1.92} \approx 306.77 \times 10^{-9} \text{ m} \)

This shortened wavelength in glass is because light travels slower in glass than in the air. The index of refraction indicates the bending and slowing down of light as it travels into the glass.

Light does not travel at the same speed in all substances. In a vacuum or air, it moves at \( 3 \times 10^8 \text{ m/s} \). However, in materials such as glass, it slows down. The speed of light in a medium is calculated using the frequency:

• \( v = f \times \lambda_{\text{medium}} \)

Substituting the values obtained in previous steps of the exercise:

• Frequency, \( f \approx 5.09 \times 10^{14} \text{ Hz} \)
• Wavelength in glass, \( \lambda_{\text{glass}} \approx 306.77 \times 10^{-9} \text{ m} \)

The speed \( v \) is:

• \( v = 5.09 \times 10^{14} \times 306.77 \times 10^{-9} \text{ m/s} \approx 1.56 \times 10^8 \text{ m/s} \)

This result shows that light travels roughly half as fast in glass as it does in air or a vacuum. Understanding the speed of light in different mediums explains how light behaves in everyday objects like lenses or water, affecting our perception and optics technology.