# How Big a Light do I Need?

Experience goes a long way, but sometimes you need to be more precise about what size of lighting instruments are required for a particular scene. Night exteriors, for example; you don’t want to find out on the day that the HMI you hired as your “moon” backlight isn’t powerful enough to cover the whole of the car park you’re shooting in. How can you prep correctly so that you don’t get egg on your face?

There are two steps: 1. determine the intensity of light you require on the subject, and 2. find a combination of light fixture and fixture-to-subject distance that will provide that intensity.

### The Required intensity

The goal here is to arrive at a number of foot-candles (fc). Foot-candles are a unit of light intensity, sometimes more formally called illuminance, and one foot-candle is the illuminance produced by a standard candle one foot away. (Illuminance can also be measured in the SI unit of lux, where 1 fc ≈ 10 lux, but in cinematography foot-candles are more commonly used. It’s important to remember that illuminance is a measure of the light incident to a surface, i.e. the amount of light reaching the subject. It is not to be confused with luminance, which is the amount of light reflected from a surface, or with luminous power, a.k.a. luminous flux, which is the total amount of light emitted from a source.)

Usually you start with a T-stop (or f-stop) that you want to shoot at, based on the depth of field you’d like. You also need to know the ISO and shutter interval (usually 1/48th or 1/50th of a second) you’ll be shooting at. Next you need to convert these facets of exposure into an illuminance value, and there are a few different ways of doing this.

One method is to use a light meter, if you have one, which you enter the ISO and shutter values into. Then you wave it around your office, living room or wherever, pressing the trigger until you happen upon a reading which matches your target f-stop. Then you simply switch your meter into foot-candles mode and read off the number. This method can be a bit of a pain in the neck, especially if – like mine – your meter requires fiddly flipping of dip-switches and additional calculations to get a foot-candles reading out of.

A much simpler method is to consult an exposure table, like the one below, or an exposure calculator, which I’m sure is a thing which must exist, but I’ll be damned if I could find one.

Some cinematographers memorise the fact that 100fc is f/2.8 at ISO 100, and work out other values from that. For example, ISO 400 is four times (two stops) faster than ISO 100, so a quarter of the light is required, i.e. 25fc.

Alternatively, you can use the underlying maths of the above methods. This is unlikely to be necessary in the real world, but for the purposes of this blog it’s instructive to go through the process. The equation is:

where

• b is the illuminance in fc,
• f is the f– or T-stop,
• s is the shutter interval in seconds, and
• i is the ISO.

Say I’m shooting on an Alexa with a Cooke S4 Mini lens. If I have the lens wide open at T2.8, the camera at its native ISO of 800 and the shutter interval at the UK standard of 1/50th (0.02) of a second…

… so I need about 12fc of light.

### The right instrument

In the rare event that you’re actually lighting your set with candles – as covered in my Barry Lyndon and Stasis posts – then an illuminance value in fc is all you need. In every other situation, though, you need to figure out which electric light fixtures are going to give you the illuminance you need.

Manufacturers of professional lighting instruments make this quite easy for you, as they all provide data on the illuminance supplied by their products at various distances. For example, if I visit Mole Richardson’s webpage for their 1K Baby-Baby fresnel, I can click on the Performance Data table to see that this fixture will give me the 12fc (in fact slightly more, 15fc) that I required in my Alexa/Cooke example at a distance of 30ft on full flood.

Other manufacturers provide interactive calculators: on ETC’s site you can drag a virtual Source Four back and forth and watch the illuminance read-out change, while Arri offers a free iOS/Android app with similar functionality.

If you need to calculate an illuminance value for a distance not specified by the manufacturer, you can derive it from distances they do specify, by using the Inverse Square Law. However, as I found in my investigatory post about the law, that could be a whole can of worms.

If illuminance data is not available for your light source, then I’m afraid more maths is involved. For example, the room I’m currently in is lit by a bulb that came in a box marked “1,650 lumens”, which is the luminous power. One lumen is one foot-candle per square foot. To find out the illuminance, i.e. how many square feet those lumens are spread over, we imagine those square feet as the area of a sphere with the lamp at the centre, and where the radius r is the distance from the lamp to the subject. So:

where

• is again the illuminance in fc,
• is the luminous power of the souce in lumens, and
• r is the lamp-to-subject distance in feet.

(I apologise for the mix of Imperial and SI units, but this is the reality in the semi-Americanised world of British film production! Also, please note that this equation is for point sources, rather than beams of light like you get from most professional fixtures. See this article on LED Watcher if you really want to get into the detail of that.)

So if I want to shoot that 12fc scene on my Alexa and Cooke S4 Mini under my 1,650 lumen domestic bulb…

… my subject needs to be 3’4″ from the lamp. I whipped out my light meter to check this, and it gave me the target T2.8 at 3’1″ – pretty close!

### Do I have enough light?

If you’re on a tight budget, it may be less a case of, “What T-stop would I like to shoot at, and what fixture does that require?” and more a case of, “Is the fixture which I can afford bright enough?”

Let’s take a real example from Perplexed Music, a short film I lensed last year. We were shooting on an Alexa at ISO 1600, 1/50th sec shutter, and on Arri/Zeiss Ultra Primes, which have a maximum aperture of T1.9. The largest fixture we had was a 2.5K HMI, and I wanted to be sure that we would have enough light for a couple of night exteriors at a house location.

In reality I turned to an exposure table to find the necessary illuminance, but let’s do the maths using the first equation that we met in this post:

Loading up Arri’s photometrics app, I could see that 2.8fc wasn’t going to be a problem at all, with the 2.5K providing 5fc at the app’s maximum distance of 164ft.

That’s enough for today. All that maths may seem bewildering, but most of it is eliminated by apps and other online calculators in most scenarios, and it’s definitely worth going to the trouble of checking you have enough light before you’re on set with everyone ready to roll!

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# The Inverse Square Law

If you’ve ever read or been taught about lighting, you’ve probably heard of the Inverse Square Law. It states that light fades in proportion to the square of the distance from the source. But lately I started to wonder if this really applies in all situations. Join me as I attempt to get to the bottom of this…

### Knowing the law

The seed of this post was sown almost a year ago, when I read Herbert McKay’s 1947 book The Tricks of Light and Colour, which described the Inverse Square Law in terms of light spreading out. (Check out my post about The Tricks of Light and Colour here.)

But before we go into that, let’s get the Law straight in our minds. What, precisely, does it say? Another excellent book, Gerald Millerson’s Lighting for Television and Film, defines it thusly:

With increased distance, the light emitted from a given point source will fall rapidly, as it spreads over a progressively larger area. This fall-off in light level is inversely proportional to the distance square, i.e. 1/d². Thus, doubling the lamp distance would reduce the light to ¼.

The operative word, for our purposes, is “spreads”.

If you’d asked me a couple of years ago what causes the Inverse Square Law, I probably would have mumbled something about light naturally losing energy as it travels. But that is hogwash of the highest order. Assuming the light doesn’t strike any objects to absorb it, there is nothing to reduce its energy. (Air does scatter – and presumably absorb – a very small amount of light, hence atmospheric haze, but this amount will never be significant on the scale a cinematographer deals with.)

In fact, as the Millerson quote above makes clear, the Inverse Square Law is a result of how light spreads out from its source. It’s purely geometry. In this diagram you can see how fewer and fewer rays strike the ‘A’ square as it gets further and further away from the source ‘S’:

Each light ray (dodgy term, I know, but sufficient for our purposes) retains the same level of energy, and there are the same number of them overall, it’s just that there are fewer of them passing through any given area.

So far, so good.

### Taking the Law into my own hands

During season two of my YouTube series Lighting I Like, I discussed Dedo’s Panibeam 70 HMI. This fixture produces collimated light, light of which all the waves are travelling in parallel. It occurred to me that this must prevent them spreading out, and therefore render the Inverse Square Law void.

This in turn got me thinking about more common fixtures – par cans, for example.

Par lamps are so named for the Parabolic Aluminised Reflectors they contain. These collect the light radiated from the rear and sides of the filament and reflect it as parallel rays. So to my mind, although light radiated from the very front of the filament must still spread and obey the Inverse Square Law, that which bounces off the reflector should theoretically never diminish. You can imagine that the ‘A’ square in our first diagram would have the same number of light rays passing through it every time if they are travelling in parallel.

Similarly, fresnel lenses are designed to divert the spreading light waves into a parallel pattern:

Even simple open-face fixtures have a reflector which can be moved back and forth using the flood/spot control, affecting both the spread and the intensity of the light. Hopefully by now you can see why these two things are related. More spread = more divergence of light rays = more fall-off. Less spread = less divergence of light rays = more throw.

So, I wondered, am I right? Do these focused sources disobey the Inverse Square Law?

### Breaking the law

Firstly, and crucially, everyone agrees that the Law describes light radiated from a point source, so any source which isn’t infinitely small will technically not be governed by the Law. In practice, says the general consensus, the results predicted by the Law hold true for most sources, unless they are quite large or very close to the subject.

If you are using a softbox, a Kinoflo or a trace frame at short range though, the Inverse Square Law will not apply.

The above photometric data for a Filmgear LED Flo-box indeed shows a slower fall-off than the Law predicts. (Based on the 1m intensity, the Law predicts the 2m and 3m intensities as 970÷2²=243 lux and 970÷3²=108 lux respectively.)

A Flickr forum contributor called Severin Sadjina puts it like this:

In general, the light will fall off as 1/d² if the size of the light source is negligible compared to the distance d to the light source. If, on the other hand, the light source is significantly larger than the distance d to the light source, the light will fall off as 1/d – in other words: slower than the Inverse Square Law predicts.

Another contributor, Ftir, claims that a large source will start to follow the Law above distances equal to about five times the largest side of the source, so a 4ft Kinoflo would obey the Law very closely after about 20ft. This claim is confirmed by Wikipedia, citing A. Ryer’s The Light Measurement Handbook.

But what about those pesky parallel light beams from the pars and fresnels?

Every forum had a lot of disagreement on this. Most people agree that parallel light rays don’t really exist in real life. They will always diverge or converge, slightly, and therefore the Law applies. However, many claim that it doesn’t apply in quite the same way.

A fresnel, according to John E. Clark on Cinematography.com, can still be treated as a point source, but that point source is actually located somewhere behind the lamp-head! It’s a virtual point source. (Light radiating from a distant point source has approximately parallel rays with consequently negligible fall-off, e.g. sunlight.) So if this virtual source is 10m behind the fixture, then moving the lamp from 1m from the subject to 2m is not doubling the distance (and therefore not quartering the intensity). In fact it is multiplying the distance by 1.09 (12÷11=1.09), so the light would only drop to 84% of its former intensity (1÷1.09²=0.84).

I tried to confirm this using the Arri Photometrics App, but the data it gives for Arri’s fresnel fixtures conforms perfectly with an ordinary point source under the Law, leaving me somewhat confused. However, I did find some data for LED fresnels that broke the Law, for example the Lumi Studio 300:

As you can see, at full flood (bottom graphic) the Law is obeyed as expected; the 8m intensity of 2,500 lux is a quarter of the 4m intensity of 10,000 lux. But when spotted (top graphic) it falls off more rapidly. Again, very confusing, as I was expecting it to fall off less rapidly if the rays are diverging but close to parallel.

A more rapid fall-off suggests a virtual point source somewhere in front of the lamp-head. This was mentioned in several places on the fora as well. The light is converging, so the intensity increases as you move further from the fixture, reaching a maximum at the focal point, then diverging again from that point as per the Inverse Square Law. In fact, reverse-engineering the above data using the Law tells me – if my maths is correct – that the focal point is 1.93m in front of the fixture. Or, to put it another way, spotting this fixture is equivalent to moving it almost 2m closer to the subject. However, this doesn’t seem to tally with the beam spread data in the above graphics. More confusion!

I decided to look up ETC’s Source Four photometrics, since these units contain an ellipsoidal reflector which should focus the light (and therefore create a virtual point source) in front of themselves. However, the data shows no deviation from the Law and no evidence of a virtual point source displaced from the actual source.

### I fought the law and the law won

I fear this investigation has left me more confused than when I started! Clearly there are factors at work here beyond what I’ve considered.

However, I’ve learnt that the Inverse Square Law is a useful means of estimating light fall-off for most lighting fixtures – even those that really seem like they should act differently! If you double the distance from lamp to subject, you’re usually going to quarter the intensity, or near as damn it. And that rule of thumb is all we cinematographers need 99% of the time. If in doubt, refer to photometrics data like that linked above.

And if anyone out there can shed any light (haha) on the confusion, I’d be very happy to hear from you!

Following on from my ‘Know Your Lights’ overview last week, today I’ll look in more detail at the first category of lamps and the various units available and when you might use them.

And that first category is incandescent lighting, commonly known as tungsten. It is the oldest, simplest and most robust lighting technology. Tungsten lamps are the cheapest to hire, the easiest to repair, and emit a smoother spectrum of light than any other artificial sources, making for the most natural skin tones. For my money, there’s no better way to artificially light a human face than by bouncing a tungsten source off polyboard.

Tungsten lighting units can be sub-categorised by the style of reflectors and/or lenses in the heads…

Open-face

 Ianiro Lilliput, a 300W open-face light Generic 800W open-face light Arrilite 1000, a 1K open-face light Generic 2K open-face light

The simplest instruments are known as ‘open-face’ because they have no lens to focus the light. By far the most common units are the 800 Watt and 2,000 Watt models. These are often referred to as ‘redheads’ and ‘blondes’ respectively, though I strongly discourage these terms for reasons touched on here. 300W models – dubbed ‘Lilliputs’ by manufacturer Ianiro – are also available, as well as 1Ks and much larger models like the Mole-Richardson Skypan 5K and Skylite 10K.

While I have lit entire no-budget features with just open-face lights, on larger productions the uneven and unfocused nature of their light makes them a poor relation of other units on the truck. They are most likely to get fired into a bounce board or used to create a little pool of light somewhere in the deep background where finesse is not needed.

Fresnel

 Arri 300W fresnel Filmgear 650W fresnel Mole Richardson 1K ‘baby’ fresnel Arri T12, a 12K fresnel

The fresnel lens was invented in the early 19th century by French physicist and engineer Augustin-Jean Fresnel in order to increase the focus and throw of lighthouse lamps. Today in the film industry, fresnel lenses can be found on tungsten, HMI and even LED fixtures.

Tungsten fresnels come in the following wattages: 150W, 300W, 650W (a.k.a. ‘tweenie’), 1K, 2K, 5K, 10K, 12K, 20K, 24K.

1Ks and 2Ks are sometimes called ‘babies’ and ‘juniors’ respectively, but confusingly those terms can also refer to whether they are the smaller location models or larger studio versions of the same wattage.

Though the fresnel lens reduces the light output a little, the beam is much more focused and can therefore create a shaft of light through smoke, which open-face lamps cannot. Hence I sometimes use tungsten fresnels to simulate hard sunlight when shooting on a stage. But beware that shadows cast by a fresnel can sometimes show up the ridges in the lens.

I often fire fresnels into bounce boards, and because their light is more focused they require less flagging to control the spill than open-face units.

On Heretiks we used numerous 300W and 650W fresnels to beef up candlelight, often placing tough-spun diffuser over them, dimming them down to warm up the colour temperature, and flickering them too.

Par (parabolic aluminised reflector)

 Par 16 (birdie) Par 38 Filmgear 4-light minibrute Mole Richardson 9-light maxibrute

Par lights use a parabolic (shaped like half a rugby ball) reflector and a lens to produce a soft-edged oval pool of light. They are extremely common in theatres, but are often used in film and TV as well.

Unlike fresnel and open-face units, par cans are referred to not by wattage but by the diameter of the bubble in eighths of an inch. So a Par 16 (a.k.a. ‘birdie’) has a 2″ bulb.

Par cans come in the following sizes: 16, 20, 36, 38, 46, 56, 64. They also come with various internal specs which affect the width of the beam.

Par cans are good for throwing shafts of light. On The Little Mermaid I used them to simulate car headlights, and as practicals (i.e. they were seen on camera) to uplight banners at the circus.

Maxibrutes (a.k.a. ‘Molepars’) are banks of multiple par 64 (1KW) lights. They come in banks of 4, 6, 9, 12 or 24. They pop up in the background of music promos quite often, because they look cool and kind of retro. I used two 9-light Maxibrutes, bounced off the tent roof, to illuminate the big top in The Little Mermaid. Some DPs like to use Maxibrutes for backlight on night exteriors. If you’re using them direct, you’ll need at least a sheet of diff to prevent multiple shadows.

Minibrutes (a.k.a. ‘fays’) are similar, but use smaller par 36 (650W) lamps.

Other

Dedolites are compact units that use a unique lens system to produce very focussed, controllable light from (most commonly) 150W bulbs. They are widely available to hire, come with in-line dimmers, and are small and light enough to be rigged overhead or in tight spots. I often use them to beef up practicals.

Source Fours or (a.k.a. ‘lekos’) are ellipsoid reflector spotlights. They feature cutters which can be used to shape the beam, they can be hired with different lenses (some of which are zoomable), and they can be fitted with gobos to project patterns. They are good for stylised pools of light or for firing into distant bounce boards without spilling light elsewhere.

Spacelights are wagon-wheel configurations of three or six 1K lamps inside a cylinder of diffusion material. They are normally used in large numbers to provide ambient toplight on stage. Click here for a brief video introduction to spacelights.

Jem Balls, or China balls, resemble Chinese paper lanterns. They come in 22″ (up to 1KW) and 30″ (up to 2KW) sizes and produce a very soft light which I personally find is never bright enough.

Bare bulbs (usually referred to as ‘globes‘) in pendant fittings can be hung from overhead or hidden behind set dressing, perhaps to beef up practicals. On Ren: The Girl with the Mark and other projects I hid some globes behind furniture to enhance the pool of light from candles.

Finally, tungsten is usually the most desirable type of bulb to use in practicals. It is commonplace when shooting a daylight interior for a spark to go around replacing the energy-saver fluorescent bulbs in the table lamps with old-school tungsten ones. The colour is much nicer, the skin tones are better as noted above, and they can be dimmed to just the right level for camera.

I’m sure I’ve missed something out – please feel free to let me know on Facebook or Twitter! Next week: HMIs.

Welcome to the first in a series of posts looking at the many types of lighting instruments in use on film and TV sets today. This is not intended to be an exhaustive or comprehensive list, but it will give you a good idea of your options, particularly if you’re moving up from smaller productions – where lighting kit is mostly borrowed – to larger ones, where you’re required to submit a lighting list to a rental house.

Some of the key considerations when choosing a lamp are:

• Colour temperature – how orange or blue the light appears – see this post for more info
• CRI – Colour Rendering Index – how full a spectrum of light is emitted, and therefore how accurately colours are rendered
• Light quality – how hard or soft the light is
• Power consumption
• Hire cost

Lamps can be divided into categories according to the means by which they produce light. Here is an overview of the main types.

Incandescent (view detailed post)

Incandescent lamps work by passing electrical current through a wire filament which becomes so hot that it glows. In the film industry they are generally referred to as ‘tungsten‘ units after the metal which the filament is made from. Common tungsten lamps include Dedolites, 1K ‘babies’ and open-face 800W and 2KW units (which have misogynous nicknames I shall not repeat here).

Pros: cheap, dimmable, extremely high CRI

Cons: very inefficient, get very hot, colour temperature changes when dimmed

Colour temperature: 3,200K

Light quality: generally hard (although certain units like Space Lights are softer)

The HMI (hydragyrum medium-arc iodide) is the most common form of high intensity discharge lamp used in the industry. It operates by creating an electrical arc between two electrodes which excites a gas. You may occasionally hear about an MSR (medium source rare-earth), which is slightly different technology, but as far as a cinematographer is concerned MSRs and HMIs are the same. They require a ballast to ignite the arc and regulate the current and voltage.

Pros: good CRI, good match for daylight, efficient

Cons: only dimmable down to 50%, expensive, heads and ballasts sometimes hum or ‘squeal’, older bulbs can vary in colour, flicker issues at certain shutter angles with magnetic ballasts

Colour temperature: 5,600K

Light quality: hard

Fluorescent (view detailed post)

Fluorescent lamps are found almost everywhere today, as strip lights in supermarkets and offices, and energy-saver bulbs in the home. Similar in principle to HMIs, electric current causes mercury vapour to emit UV light which is translated into the visible spectrum by the phosphor coating on the tube. Kino Flo pretty much has the monopoly on fluorescent lighting for the film industry. Like HMIs, fluorescents require a ballast.

Pros: reasonable CRI from Kino Flos (appalling CRI from domestic/commercial fixtures), very efficient, get warm but not hot

Cons: limited dimming, high fall-off of light

Colour temperature: 5,500K and 3,200K tubes available

Light quality: soft

Gradually replacing tungsten as the most common lamps found on no-budget shoots, LED (light emitting diode) units contain semi-conductors that emit light when their electrons reconfigure. The technology is advancing rapidly, but there is currently a wide range of LED lamps on the market, varying greatly in price and corresponding quality.

Pros: extremely efficient, barely get warm, can run off batteries, almost fully dimmable, some models have adjustable colour temperature

Cons: CRI ranges from almost acceptable in the expensive models to downright shocking in the cheaper ones

Colour temperature: varies

Light quality: varies

Though there are other types of lighting, like xenon, metal-halide and HEP (high efficiency plasma), the above four are the main ones you will encounter on film and TV sets today. Over the next few weeks I’ll look at each of those types in more detail, listing many of the specific units available in each category and their applications.

By the way, if your budget is too tight to hire film lamps of any kind, you may want to check out my post on lighting without movie lamps.