Answer to Question #250046 in Mechanics | Relativity for John

Question

 Convert the following wavelengths to frequencies (Hz):

a. 0.71 μm

b. 31.20 μm

c. 419 nm

d. 1385 nm

e. 17.31 cm 

Answer 1

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

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

$\text{Since no propagation medium is specified, the }$

$\text{default is an electromagnetic wave in a vacuum.}$

$c \approx 3*10^8\frac{m}{c}$

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

$a. \lambda= 0.71 μm = 0.71*10^{-6}m$

$f= \frac{c}{\lambda}=\frac{3*10^8}{0.71*10^{-6}}=4.23*10^{14}Hz$

$b. \lambda = 31.20 μm = 31.2*10^{-6}m$

$f= \frac{c}{\lambda}=\frac{3*10^8}{31.2*10^{-6}}=9.62*10^{12}Hz$

$c. \lambda= 419 nm= 419*10^{-9}m$

$f= \frac{c}{\lambda}=\frac{3*10^8}{419*10^{-9}}=7.16*10^{14}Hz$

$d. \lambda= 1385 nm= 1385*10^{-9}m$

$f= \frac{c}{\lambda}=\frac{3*10^8}{1385*10^{-9}}=2.17*10^{14}Hz$

$e. \lambda=17.31 cm =17.31*10^{-2}m$

$f= \frac{c}{\lambda}=\frac{3*10^8}{17.31*10^{-2}}=1.73*10^{9}Hz$