Question

A certain type of laser emits light that has a frequency of 7.2 × 1014 Hz. The light, however, occurs as a series of short pulses, each lasting for a time of 3.7 × 10-11 s. (a) How many wavelengths are there in one pulse? (b) The light enters a pool of water. The frequency of the light remains the same, but the speed of the light slows down to 2.3 x 108 m/s. How many wavelengths are there now in one pulse?

Answer 1

a) 26 640

b) 26 640

Step-by-step explanation:

Hello!

a)

We need first to know the wavelength of the laser, and this can be known from the relation between wavelength frequency and the velocity of ligth c = fλ:

λ = c/f = (3x10^8 m/s) / (7.2 x 10^14 Hz) = 4.166 x 10^-7 m = 416.6 nm

Now, we need to know the spatial length of the pulse, and we are going to calculate it as follows:

d = c t = (3x10^8 m/s) (3.7 x 10^-11 s) =1.11 x 10^-2 m

To know how many wavelengths are in one pulse its enough to divide these two quantityes:

d/λ =(ct)/(c/f) = ft = (7.2 x 10^14 Hz) (3.7 x 10^11 s) = 26 640

b)

From the previous result we said that the number of wavelengths in one pulse is just the division of d/λ which is the same as t*f, which in turn is independent of the velocity of light, therefore, the number of wavelengths in one pulse remains the same