The Wavelength Calculator applet provides an interactive way to explore the spectrum of electromagnetic radiation and evaluate the wavelength by varying the frequency. This applet is written in JAVA 2.0 and it will run on any recent web browser with the appropriate Java plug-in installed.
After start up, the applet appears in its default page dedicated to the visible portion of the frequency spectrum. The graphical user interface (GUI) of this applet consists of five parts: Title Panel, Control Panel, Display Panel, Unit Panel and Input Panel.
It is possible to display the wavelength in any of the practical units used in engineering and physics. The length units can be changed by clicking on the desired button in the Unit Panel, with automatic update of the Display Panel. A box appears on the right of the Unit Panel to remind of the conversion factor between meters and the selected unit.
The desired frequency can be entered by moving the sliders in the input panel. For small increments, click on the small black arrowheads at the ends of the slider. For larger increments, click in the space on the left or right of the cursor. Click and hold after positioning the mouse on the slider cursor to drag right or left.
The main yellow slider spans the entire portion of the selected frequency spectrum. The Visible Spectrum is completely confined in the tera-Hertz frequency range. Therefore, the main slider is simply programmed to increment uniformly the frequency as it is moved. For other spectrum selections, where different multiples of Hertz are involved, the main slider is programmed to give non-uniform frequency variation to provide sufficient resolution in all the frequency bands. When appropriate, relevant information on the frequency band appears in the space under the sliders.
The small white slider adds three decimals to frequency to fine tune the input. This slider always provides uniform increments, adding extra decimals from 000 to 999.
For wave propagation in a different dielectric material, one can modify the relative dielectric constant by entering the desired value in the input box and then clicking the UPDATE button. The phase velocity for the different dielectric will be automatically updated in the Unit Panel.
Note that this applet uses internally the best available experimental value for the phase velocity of light in vacuum, 2.997924579998582 x 108 m/s, rather than the approximation 3.0 x 108 m/s which is often used in textbooks.
This new version also includes the possibility to specify a lossy medium by entering the desired value of the material conductivity in the corresponding input box. Click the UPDATE button to calculate the new values of wavelength and phase velocity.
Keep in mind that both dielectric constant and conductivity are in general functions of frequency for a realistic material. Values should be changed appropriately when scanning different spectrum ranges.
The phase velocity and the wavelength for a lossy medium are obtained using the following general formulas
where the circular frequency and the wave number are given by
The medium dielectric constant or permittivity is
with the vacuum permittivity
We consider here always the case of non-magnetic materials, with magnetic permeability equal to the vacuum permeability
Other frequency ranges can be selected from the drop menu in the Control Panel.
The Optical Spectrum expands the Visible Spectrum by adding the Infra-Red (IR) range and the Ultra-Violet (UV) range.
The Radio Spectrum provides the frequency range below the Infra-Red, and it is subdivided into the standard bands for radio communications.
The Full Spectrum shows the complete practical range of electromagnetic wave frequencies, extending from zero all the way up to Gamma Rays. The Full Spectrum is subdivided into ranges corresponding to multiples of Hertz.
The Display Panel is arranged to resemble digital displays of calculators and measurement equipment. This rendition of the numbers facilitates the observation of the results when the input is changed continuously.
The color scheme of the Display Panel can be changed from LED look-alike (red on black) to LCD look-alike (black on gray) by simply clicking on the panel itself.