To calculate the number of complete vibrations (cycles) in a wave train of light, we can use the formula:
Number of cycles = (Time / Period)
Given: Wavelength (λ) = 520 nm Time (t) = 430 ps
First, let's convert the given values to the appropriate units:
Wavelength (λ) = 520 nm = 520 × 10^(-9) meters (since there are 1 billion nanometers in a meter) Time (t) = 430 ps = 430 × 10^(-12) seconds (since there are 1 trillion picoseconds in a second)
Next, we need to calculate the period (T) of the wave using the formula:
Period (T) = λ / v
Where v represents the speed of light, which is approximately 3 × 10^8 meters per second.
Period (T) = (520 × 10^(-9)) / (3 × 10^8) = 1.733 × 10^(-15) seconds
Finally, we can calculate the number of cycles:
Number of cycles = (Time / Period) = (430 × 10^(-12)) / (1.733 × 10^(-15))
Number of cycles ≈ 248,555.69
Therefore, there are approximately 248,556 complete vibrations (cycles) in a wave train of light with a wavelength of 520 nm emitted by a laser for a time of 430 ps.