To calculate the wavelength ($\lambda$) of light, you can use the relationship between the speed of light ($c$), its frequency ($f$), and its wavelength:

$\lambda = \frac{c}{f}$

Given:

• Speed of light ($c$) = $3.0 \times 10^8 \, \text{m/s}$
• Frequency ($f$) = $5.2 \times 10^{12} \, \text{Hz}$

Calculation:

$\lambda = \frac{3.0 \times 10^8}{5.2 \times 10^{12}}$

1. Divide the coefficients: $\frac{3.0}{5.2} \approx 0.577$

2. Subtract the exponents: $10^8 - 10^{12} = 10^{-4}$

$\lambda \approx 0.577 \times 10^{-4} \, \text{m}$

3. Rewrite in scientific notation: $\lambda \approx 5.77 \times 10^{-5} \, \text{m}$

Final Answer:

The wavelength of the light is:

$\lambda = 5.77 \times 10^{-5} \, \text{m} \, \text{(or 57.7 µm)}.$

Would you like further clarification on this calculation or more examples?

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Here are 5 related questions for deeper exploration:

1. What is the relationship between wavelength, frequency, and energy in electromagnetic waves?
2. How does the wavelength of light influence its color or type (e.g., infrared, visible)?
3. If the frequency doubles, what happens to the wavelength?
4. How is this formula applied in determining the properties of X-rays or radio waves?
5. How do different mediums affect the speed of light and wavelength?

Tip: Always ensure units are consistent (e.g., meters, Hz) when using wave equations.