Question

For a certain light there are $2 \times {10^3}$ waves in 1.5 mm in air. The wavelength of light is:
A. 750 nm
B. \[75\;{\rm{A}}^\circ \]
C. \[750\;{\rm{A}}^\circ \]
D. \[7.5 \times {10^{ - 7}}\;{\rm{A}}^\circ \]

Answer 1

Hint: The wavelength is the number distance between the two crests or two troughs in any frequency. The wavelength is taken as mm, cm, m as the units to calculate. The frequency is defined as vibrations that form in waves per second time.


Complete step by step solution
Given:
The number of waves in a certain light is $n = 2 \times {10^3}$.
The length of the air is
\[\begin{array}{c}
l = 1.5\;{\rm{mm}}\\
{\rm{ = 1}}{\rm{.5}} \times \dfrac{{1\,{\rm{m}}}}{{1000\,{\rm{mm}}}}\\
 = {\rm{1}}{\rm{.5}} \times {10^{ - 3}}\,{\rm{m}}
\end{array}\].
The equation to find the wavelength of the light is,
\[\lambda = \dfrac{l}{n}\]
It means the wavelength of the light is defined as the ratio of the length of the waves in the air to the number of waves in a certain light.
Substitute the values in the above equation.
\[\begin{array}{c}
\lambda = \dfrac{l}{n}\\
 = \dfrac{{1.5 \times {{10}^{ - 3}}\,m}}{{2 \times {{10}^3}}}\\
 = 7.5 \times {10^{ - 7}}\,{\rm{m}}\\
 = \left( {7.5 \times {{10}^{ - 7}}\,{\rm{m}}} \right)\left( {\dfrac{{1\;{\rm{nm}}}}{{{{10}^{ - 9}}\;{\rm{m}}}}} \right)\\
 = 750\;{\rm{nm}}
\end{array}\]
Therefore, the wavelength is \[750\;\,{\rm{nm}}\] that means the option (a) is correct.


Note: Before substituting the values, be sure the units are according to the requirement. The conversion of millimeters to the meters can be done by dividing 1000.