Wave, Field & Optics Calculators

What Wave, Field & Optics Calculators Solve

Radio waves, light, and magnetic fields run on the same physics. Wave, Field & Optics Calculators cover the conversions that come up across all three: wavelength, decibels, penetration depth, refraction, and beam intensity.

These are the tools you reach for before the design work starts. Cutting an antenna, plating a cavity, or aiming a laser all begin with one of these numbers.

Frequency and Wavelength

The Frequency to Wavelength Calculator converts between the two and gives the half-wave, quarter-wave, and 5/8-wave element lengths used in antenna work.

In free space, wavelength in metres is 300 divided by frequency in megahertz. At 146 MHz that is 2.05 m, which is why the band is called 2 metres. A quarter-wave element works out at 51 cm.

Real conductors are shorter than the theoretical figure. A velocity factor near 0.95 for wire brings that quarter wave to about 49 cm, and coaxial cable runs near 0.66, so an electrical quarter wavelength of cable is far shorter than the free-space number.

The same conversion works at microwave and optical frequencies. At 2.45 GHz the wavelength is 12.2 cm, which is what sets the size of a microwave oven cavity and its hot spots.

Working in Decibels

The Decibel Calculator converts power and voltage ratios into dB, and adds dBm, VSWR, and neper values.

Power ratios use ten times the log. Voltage ratios use twenty times the log, because power follows voltage squared. Mixing the two is the most common decibel error.

Plain dB is a ratio with no reference. dBm fixes the reference at 1 mW, so 0 dBm is 1 mW and 30 dBm is 1 W. That is why levels in dBm can be added and subtracted through a chain, while bare dB figures only describe gain or loss.

Skin Depth

The Skin Depth Calculator gives how far alternating current penetrates a conductor, plus surface resistance and impedance, from resistivity, permeability, and frequency.

Skin depth is where current density has fallen to about 37% of the surface value. It scales with the inverse square root of frequency, so four times the frequency halves the depth.

Those numbers decide a lot of practical choices. At 1 MHz, copper thicker than a few tenths of a millimetre adds mass without carrying more current. For RF traces, widening beats thickening, because the extra copper sits below the conducting layer.

Plating follows the same rule. Copper-plating a steel cavity works because the current never reaches the steel, and plating is usually specified at 10 to 20 times the skin depth. Aluminium’s skin depth runs about 30% deeper than copper’s at the same frequency.

Fields and Forces

The Lorentz Force Calculator gives the force on a charge moving through electric and magnetic fields, splitting electric force, magnetic force, and the total.

The electric part acts along the field and does not care about motion. The magnetic part depends on velocity and acts at right angles to both the velocity and the field, which is why it bends a path instead of speeding it up.

That difference explains cyclotrons, mass spectrometers, and the deflection coils in old CRT displays. It also sets the drift velocity and field energy density the tool reports.

Refraction and Light

The Snell’s Law Calculator handles refraction: the first refractive index times the sine of the incoming angle equals the second index times the sine of the outgoing angle.

Past a certain angle, light coming from the denser medium stops leaving at all. That critical angle is about 41.8° for glass with an index of 1.5, and 48.8° for water at 1.33. Total internal reflection above that angle is what keeps light inside an optical fibre.

The Laser Power Density Calculator divides beam power by spot area. A 5 mW pointer focused to a 1 mm spot gives about 0.64 W per square centimetre, and halving the spot diameter quadruples that figure.

Power density, not total power, is what damages a surface or an eye. A low-power beam tightly focused can exceed the intensity of a much larger beam spread wide.

The Convert MCD to Lumens tool goes from millicandela, an intensity in one direction, to lumens, the total light output. The link is the beam angle, so the same 5,000 mcd LED gives about 1.1 lumens in a 30° beam and far more when the beam is wide.

Common Mistakes

Using 10 log for voltage ratios. Voltage needs 20 log, so the answer comes out half as large in dB.

Cutting elements to free-space length. Velocity factor makes real conductors and cable shorter than the calculation.

Paying for thick copper at RF. Above a megahertz the current rides in the top tens of microns.

Comparing LEDs by millicandela. A narrow beam inflates the figure, so lumens is the fair comparison.

Wave and Optics FAQs

How do I convert frequency to wavelength?

Divide 300 by the frequency in megahertz for the wavelength in metres. At 146 MHz that gives 2.05 m, and a quarter wave is 51 cm. Multiply by the velocity factor for the real material, near 0.95 for bare wire and about 0.66 for common coax, before cutting anything.

When do I use 10 log instead of 20 log?

Use 10 log for power ratios, in watts or milliwatts, and 20 log for voltage or current ratios. Both describe the same change: doubling voltage is 6 dB, and doubling power is 3 dB. Mixing them up produces an answer that is out by a factor of two in dB.

What is skin depth in copper at 1 MHz?

About 66 µm, which is where current density drops to 37% of the surface value. At 60 Hz it is 8.5 mm, and at 2.4 GHz only 1.3 µm. Since depth follows the inverse square root of frequency, four times the frequency halves it. Conductors thicker than a few skin depths gain almost nothing in AC resistance.

What is the critical angle for glass?

About 41.8° for glass with a refractive index of 1.5, measured from the normal inside the glass. Beyond that angle light reflects entirely back rather than refracting out. Water at 1.33 has a critical angle near 48.8°, and a higher index gives a smaller angle, which is why fibre cores are made denser than their cladding.

How do I convert millicandela to lumens?

You need the beam angle as well as the intensity, because candela measures brightness in one direction while lumens measure total output. A 5,000 mcd LED with a 30° beam gives roughly 1.1 lumens. The same intensity spread over 120° yields many times more, which is why narrow-beam LEDs advertise impressive millicandela figures.

Why does laser power density matter more than power?

Damage follows energy per unit area. A 5 mW beam in a 1 mm spot is about 0.64 W per square centimetre, and focusing it to 0.5 mm raises that to roughly 2.5 W per square centimetre with no change in power. The eye focuses a beam further still, which is why milliwatt lasers carry hazard ratings.