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(Use c=f*lamda) calculate the frequency of green light with 545 nm (1nm = 10 to the -9th power)

physics
Guest Apr 28, 2015

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 #1
avatar+18712 
+10

(Use c=f*lamda) calculate the frequency of green light with 545 nm (1nm = 10 to the -9th power)

$$\boxed{\; c = f\cdot \lambda \qquad \text{ or }\qquad \lambda=\dfrac{c}{f} \qquad \text{ or }\qquad f=\dfrac{c}{\lambda}
\qquad
\begin{array}{rcl}
c &=& \small{\text{ speed of light in vacuum }} \\
\lambda &=& \small{\text{ wavelength }} \\
f &=& \small{\text{ wave's frequency }}
\end{Array}
\; }$$

 

$$\small{\text{
$
\begin{array}{rclcc}
f &=& \dfrac{c}{\lambda} \quad & \quad c = 299\,792\,458 ~ \mathrm{\dfrac{m}{s}} \quad & \quad \lambda = 545 ~ \mathrm{nm} = 545\cdot 10^{-9} ~ \mathrm{m} \\\\
f&=& \dfrac{ 299\,792\,458 ~ \mathrm{\dfrac{m}{s}} }{545\cdot 10^{-9} ~ \mathrm{m} } \\\\
f&=& \dfrac{ 2.99\,792\,458\cdot 10^{8} ~ \mathrm{\dfrac{m}{s}} }{545\cdot 10^{-9} ~ \mathrm{m} } \\\\
f&=& \dfrac{ 2.99\,792\,458 }{545}\cdot 10^{8}\cdot 10^{9} ~ \mathrm{\dfrac{1}{s}} \\\\
f &=& 0.00550077905\cdot 10^{17} ~ \mathrm{\dfrac{1}{s}} \\\\
f &=& 0.550077905\cdot 10^{-2}\cdot 10^{17} ~ \mathrm{\dfrac{1}{s}} \\\\
f &=& 0.550077905\cdot 10^{15} ~ \mathrm{\dfrac{1}{s}} \\\\
f &=& 0.550077905\cdot 10^{15} ~ \mathrm{ Hz } \\\\
f &=& 0.550077905 ~ \mathrm{ PHz } \quad & \quad \mathrm{ PHz } = \mathrm{ Petahertz }\\\\
f &=& 550.077905 ~ \mathrm{ THz } \quad & \quad \mathrm{ THz } = \mathrm{ Terahertz }
\end{array}
$}}$$

 

 

heureka  Apr 28, 2015
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1+0 Answers

 #1
avatar+18712 
+10
Best Answer

(Use c=f*lamda) calculate the frequency of green light with 545 nm (1nm = 10 to the -9th power)

$$\boxed{\; c = f\cdot \lambda \qquad \text{ or }\qquad \lambda=\dfrac{c}{f} \qquad \text{ or }\qquad f=\dfrac{c}{\lambda}
\qquad
\begin{array}{rcl}
c &=& \small{\text{ speed of light in vacuum }} \\
\lambda &=& \small{\text{ wavelength }} \\
f &=& \small{\text{ wave's frequency }}
\end{Array}
\; }$$

 

$$\small{\text{
$
\begin{array}{rclcc}
f &=& \dfrac{c}{\lambda} \quad & \quad c = 299\,792\,458 ~ \mathrm{\dfrac{m}{s}} \quad & \quad \lambda = 545 ~ \mathrm{nm} = 545\cdot 10^{-9} ~ \mathrm{m} \\\\
f&=& \dfrac{ 299\,792\,458 ~ \mathrm{\dfrac{m}{s}} }{545\cdot 10^{-9} ~ \mathrm{m} } \\\\
f&=& \dfrac{ 2.99\,792\,458\cdot 10^{8} ~ \mathrm{\dfrac{m}{s}} }{545\cdot 10^{-9} ~ \mathrm{m} } \\\\
f&=& \dfrac{ 2.99\,792\,458 }{545}\cdot 10^{8}\cdot 10^{9} ~ \mathrm{\dfrac{1}{s}} \\\\
f &=& 0.00550077905\cdot 10^{17} ~ \mathrm{\dfrac{1}{s}} \\\\
f &=& 0.550077905\cdot 10^{-2}\cdot 10^{17} ~ \mathrm{\dfrac{1}{s}} \\\\
f &=& 0.550077905\cdot 10^{15} ~ \mathrm{\dfrac{1}{s}} \\\\
f &=& 0.550077905\cdot 10^{15} ~ \mathrm{ Hz } \\\\
f &=& 0.550077905 ~ \mathrm{ PHz } \quad & \quad \mathrm{ PHz } = \mathrm{ Petahertz }\\\\
f &=& 550.077905 ~ \mathrm{ THz } \quad & \quad \mathrm{ THz } = \mathrm{ Terahertz }
\end{array}
$}}$$

 

 

heureka  Apr 28, 2015

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