| E | = ε μ | H | {\displaystyle \left|\mathbf {E} \right|={\sqrt {\varepsilon \over \mu }}\left|\mathbf {H} \right|\,\!}

This article summarizes equations used in optics, including geometric optics, physical optics, radiometry, diffraction, and interferometry.

Lens focal length from refraction indices 1 f = ( n l e n s n m e d − 1 ) ( 1 r 1 − 1 r 2 ) {\displaystyle {\frac {1}{f}}=\left({\frac {n_{\mathrm {lens} }}{{n}_{\mathrm {med} }}}-1\right)\left({\frac {1}{r_{1}}}-{\frac {1}{r_{2}}}\right)\,\!}

1 x 1 + 1 x 2 = 1 f = 2 r {\displaystyle {\frac {1}{x_{1}}}+{\frac {1}{x_{2}}}={\frac {1}{f}}={\frac {2}{r}}\,\!}

The LED controller also offers a current-controlled mode for continuous light, as well as voltage-controlled mode for short, precise and powerful flashes. The 4 channels can be controlled separately or coupled.

The CTR-51 allows very short flash and response times in the µs range. The current and operating mode or the flash time can be set via two rotary switches in the housing. The CTR-51 can be completely configured via a PC using the RS232 interface.

LED controller from MBJ are the ideal accessories for external LED lighting control. Our controllers are easy to mount on a DIN rail and connect with 24V. Settings are done directly on the controller or via RS232. Our 4-channel controller offers an Ethernet connection with which it is possible to communicate via the Modbus protocol.

Christmas lights with 8 Functioncontroller

Φ = ∭ L ν d ν ( e ^ ∠ ⋅ d A ) d Ω {\displaystyle \Phi =\iiint L_{\nu }\mathrm {d} \nu \left(\mathbf {\hat {e}} _{\angle }\cdot \mathrm {d} \mathbf {A} \right)\mathrm {d} \Omega \,\!}

Image distance in a spherical mirror n 1 x 1 + n 2 x 2 = ( n 2 − n 1 ) r {\displaystyle {\frac {n_{1}}{x_{1}}}+{\frac {n_{2}}{x_{2}}}={\frac {\left(n_{2}-n_{1}\right)}{r}}\,\!}

4 Channel8 Function chaseControllerwith Push Button

At a spherical surface: I = P 0 Ω | r | 2 {\displaystyle I={\frac {P_{0}}{\Omega \left|r\right|^{2}}}\,\!}

The CTR-50 allows simple and precise current adjustments. The desired current is set manually via two rotary controls. Alternatively, the CTR-50 can be completely configured via a PC using the RS232 interface.

These ratios are sometimes also used, following simply from other definitions of refractive index, wave phase velocity, and the luminal speed equation:

n 1 n 2 = v 2 v 1 = λ 2 λ 1 = ε 1 μ 1 ε 2 μ 2 {\displaystyle {\frac {n_{1}}{n_{2}}}={\frac {v_{2}}{v_{1}}}={\frac {\lambda _{2}}{\lambda _{1}}}={\sqrt {\frac {\varepsilon _{1}\mu _{1}}{\varepsilon _{2}\mu _{2}}}}\,\!}

In astrophysics, L is used for luminosity (energy per unit time, equivalent to power) and F is used for energy flux (energy per unit time per unit area, equivalent to intensity in terms of area, not solid angle). They are not new quantities, simply different names.

The adapter cable makes it easier to set up the CTR-50 and CTR-51 controller series via RS-232. Simply connect the three open cable ends to the RS-232 port of the controller. The USB-to-RS232 converter is then plugged into the USB port of the computer - the controller can now be adapted to your requirements using serial communication software (e.g. HTerm).

Φ = ∬ E ν d ν ( e ^ ∠ ⋅ d A ) {\displaystyle \Phi =\iint E_{\nu }\mathrm {d} \nu \left(\mathbf {\hat {e}} _{\angle }\cdot \mathrm {d} \mathbf {A} \right)}

Far-field (Fraunhofer) A ( r ) ∝ e i k r 4 π r ∬ a p e r t u r e E i n c ( r ′ ) e − i k [ sin ⁡ θ ( cos ⁡ ϕ x ′ + sin ⁡ ϕ y ′ ) ] d x ′ d y ′ {\displaystyle A\left(\mathbf {r} \right)\propto {\frac {e^{ikr}}{4\pi r}}\iint _{\mathrm {aperture} }E_{\mathrm {inc} }\left(\mathbf {r} '\right)e^{-ik\left[\sin \theta \left(\cos \phi x'+\sin \phi y'\right)\right]}\mathrm {d} x'\mathrm {d} y'}

What does "integrated" mean? The -s controller is installed directly in the housing to save space and enables slim installation dimensions of the lighting. Commissioning via plug'n'play is quick and easy, and with no less than four operating modes, the -s Controller is a real all-rounder.

A ( r ) ∝ ∬ a p e r t u r e E i n c ( r ′ )   e i k | r − r ′ | 4 π | r − r ′ | d x ′ d y ′ {\displaystyle A\left(\mathbf {r} \right)\propto \iint _{\mathrm {aperture} }E_{\mathrm {inc} }\left(\mathbf {r} '\right)~{\frac {e^{ik\left|\mathbf {r} -\mathbf {r} '\right|}}{4\pi \left|\mathbf {r} -\mathbf {r} '\right|}}\mathrm {d} x'\mathrm {d} y'}

The popular -s controller also as a cable-integrated variant, e.g. to retrofit standard lighting without an internal controller (-x).

All MBJ standard lights are available with integrated 4-mode controller - one of the most popular and customer appreciated features in our portfolio.

The CTR-52 allows to control up to four LED channels via one controller. This controller is set up via Modbus. A Windows-based client supports the simple integration and programming of the controller and offers ready-made sequence modes for special applications such as Shape from Shading.