Calculating Beat Frequency from Wavelengths with Approximation

[keith river]

Two lasers are incident on a photodetector, one has a wavelength of 780.56160 nm the other has a slightly shorter wavelength. They produce a beat frequency of 460 Hz.

Attempt
df = f2 - f1 = c ((1/ lambda1) - (1/ lambda2))
= c ((lambda1 - lambda2) / (lambda1 * lambda2))

Is it ok to approximate that the above is equal to
(c * d lambda) / lambda1^2

If I can then I could rearrange for
d lambda = lambda1^2 * (df / c)

and then getting lambda 2 would be easy, but I'm not sure if this is an ok approximation or if there is another way to approach this problem.

 

[NateD]

Yes, this is an acceptable approximation. You can use it to calculate the difference in wavelength between the two lasers as dλ = λ1^2*(df/c). Then you can find the wavelength of the second laser by subtracting the difference from the wavelength of the first laser, λ2 = λ1 - dλ.