An electric searchlight places a bright source near the focus of a reflector to send light in a concentrated direction. This example shows the housing, carbon arc, front glass and pedestal of an early searchlight arrangement, alongside a separate ideal parabolic-ray diagram. Its calculator estimates axial luminous intensity from assumed luminance, aperture diameter and an effective optical factor.
Electric Searchlight Interactive Calculator
Explore an early arc searchlight and ideal parabolic reflection. Compare aperture diameter, assumed source luminance and an effective optical factor.
Equation Used
- Uniform effective aperture luminance in the viewing direction.
- Circular projected aperture and supplied effective optical factor.
- Point focus and ideal parabola only in the ray demonstration.
- No electrical power, glare, atmosphere or range prediction.
Uniform effective-aperture luminance approximation. Intensity is not power, total flux or range.
The arc, reflector and adjustable housing
Hiscox movement 745 illustrates an Edison searchlight with an arc ahead of a concave reflector, a protective flat front glass and an adjustable mount. The cutaway follows that arrangement and exposes the carbon holders inside the housing.
The lamp pitches about its mount while the pedestal remains stationary. This slow aiming movement illustrates the mechanism; it is not a simulation of a particular motorized aiming system. The carbon-feed regulator is not modeled.
The lower diagram isolates an ideal parabolic reflector. Rays leave its point focus, meet the reflector and emerge parallel to the optical axis. The hardware is omitted from that optical detail so the reflection geometry stays readable. The dots indicate direction, not the speed of light.
A finite real arc, imperfect focus and nonideal surfaces produce a beam with spread. The illustration does not imply a perfectly parallel, loss-free beam from an actual lamp.
Compare aperture and assumed luminance
The source-luminance input and optical factor define a simplified effective luminance across the projected aperture. The calculation assumes that approximation is appropriate for the optical system being compared.
Aperture area grows with diameter squared. At fixed luminance and factor, doubling diameter therefore quadruples the estimated axial luminous intensity. Changing source luminance or the optical factor changes the estimate linearly.
The housing is framed at a readable size as diameter changes; the diameter label and calculation carry the entered measurement. The picture is not a dimensioned housing, electrode or feed-mechanism design.
Intensity from projected luminous area
For diameter D in inches, D_m=0.0254D metres and projected aperture area A=πD_m²/4. With L in million candela per square metre, the ideal axial intensity is LA in million candela. Applying the supplied factor η gives I=LAη.
This is a uniform effective-aperture-luminance approximation. The difference LA−I is the reduction in this axial-intensity estimate; it is not heat dissipation or lost electrical power.
Luminous intensity is measured in candela. It differs from luminous flux in lumens and electrical or radiant power in watts. The result describes intensity along the optical axis, rather than the total energy emitted by the lamp.
No beam solid angle is entered here. The calculator therefore cannot determine total flux from the axial result or predict beam divergence, illuminance at a target or useful viewing range.
A 24-inch aperture comparison
A 24-inch aperture has diameter 0.6096 m and projected area about 0.291864 m². With assumed luminance 120 Mcd/m², LA is approximately 35.02 Mcd. A 72% effective optical factor gives approximately 25.22 Mcd and an intensity reduction of 9.81 Mcd.
At 48 inches with the same assumptions, all intensity values become four times larger. Changing only the factor from 72% to 60% lowers the estimated intensity from about 25.22 to 21.01 Mcd.
These are conditional comparisons, not measured ratings of the historical Edison lamp, a naval searchlight or a particular modern product.
Where the simple estimate stops
The supplied factor combines optical reductions into one number. It is not computed from glass transmission, mirror reflectance, lamp blockage, source placement or scatter. A detailed optical model or photometric measurement is needed to establish those effects.
The model does not calculate arc current, electrode consumption, ignition voltage, cooling, electrical efficiency, beam divergence or atmospheric attenuation. Focus tolerances, operating current, maintenance intervals and useful range depend on the particular lamp and optical system.
Image brightness is illustrative. Increasing the entered intensity does not attempt to reproduce physical glare on the display.
Electric searchlight questions
Why do reflected rays run parallel?
That is the ideal point-focus property of a parabolic reflector. A real source and real optics create a beam with spread.
Is the result electrical power?
No. It is an estimate of axial luminous intensity in million candela.
Why does doubling diameter give four times the result?
Projected circular area is proportional to the square of diameter, with the other assumptions held constant.
Does the factor predict every optical loss?
No. It is supplied by the user as one effective multiplier.
Can this predict how far the light reaches?
No. That needs beam distribution, atmosphere, target properties and a definition of useful illumination.
References
- Gardner D. Hiscox, Mechanical Movements, Powers, Devices and Appliances (1901), printed page 198, movement 745 — Edison searchlight construction.
- Edmund Optics: Precision Parabolic Reflectors — collimation from a source at the focus.
- CIE International Lighting Vocabulary: luminance — luminous intensity and projected area.
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