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Variance of Intensity with Depth

Contents:

  1. Light Intensity and Physics 101
    by booth-at-lvld.hp.com () (26 Apr 1994)
  2. AQUAMYTH #1 More Light for Deep Tanks -- NOT!
    by huntley-at-ix.netcom.com (Wright Huntley ) (Sat, 21 Oct 1995)
  3. More Light for Deep Tanks - NOT!
    by nfrank-at-nando.net (Neil Frank) (Sun, 22 Oct 95)
  4. Light vs. Depth
    by Erik Olson (Sun, 22 Oct 1995)
    (e-mail)
  5. AQUAMYTH #1 lights in deep tanks
    by Stephen.Pushak-at-saudan.HAC.COM (Sun, 22 Oct 95)
  6. Light attenuation by plants
    by nfrank-at-nando.net (Neil Frank) (Sat, 18 Nov 95)
  7. Lighting Myths, Revisited!
    by Erik Olson (e-mail) ()

Light Intensity and Physics 101

by booth-at-lvld.hp.com ()
Date: 26 Apr 1994
Newsgroup: rec.aquaria,alt.aquaria,sci.aquaria

Dustin Lee Laurence (laurence-at-cco.caltech.edu) wrote:
> Grant.Gussie-at-phys.utas.edu.au (Grant Gussie) writes:
> >The famous inverse square law applies ONLY to a point source of light that
> In fact, the 1/r intensity rule for line sources is not terribly
> relevant either as far as fluorescent lit reefs is concerned.  1/r^2
> is more than accurate enough for considering metal halide lighting,
> which is for these purposes a small number of point sources which can
> be superimposed incoherently. 

Here's what I measured last night.  These were quick and dirty 
measurements made after consuming a lovely cocktail and as such,
probably don't qualify for the Journal of the Society of Lighting 
Engineers.  But they should be good enough to add fuel to the fire :-).  
I didn't get around to the MH light yet, maybe tonight.  

Executive summary: Light intensity from a dual 40w shoplight is inversely
proportional to the distance from the bulb.  Triton "Enhancers" (shiny
metal reflectors) don't enhance much compared to a plain white reflector.
Light intensity in an aquarium is tough to predict. 

----------------------------------------------------------------------------
                  Light Intesity in Air
                  ---------------------

                                    Distance from center of bulb (cm)
                                      10       20      40     80    120
------------------------------------------------------------------------
1. Sears shoplight; 1 Triton,       10,800    5,300   2,400   940   530 
   1 Coralife TriChromatic

1.5 measured at end of fixture       6,900    3,400   1,600   780   450


2. Sears shoplight, 1 Triton,       15,050    8,000   3,600  1,520  810
   1 Ultra Trilux

3. Sears shoplight, 1 Triton,       13,500    7,200   3,100  1,370  780
   1 Ultra Trilux

4. Triton Enhancer, 1 Triton,       13,300    8,400   4,100  1,630  830
   1 Ultra Trilux

Notes:
1. All fixtures use magnetic ballasts.
2. All measurements made at center of fixture (except 1.5).
3. Bulbs are various ages.
4. Intensity values are lux (lumens per square meter).
5. Sears shoplight reflector is "w" shaped; Triton Enhancer is
   "sort of" hemispherical.  Enhancer seems to help a little at longer
   distances. 
----------------------------------------------------------------------------

                  Light Intesity in Water
                  -----------------------

                                    Distance below surface of water (cm)
                                       0       10      20     30     40
------------------------------------------------------------------------
1. Bulb and fixture from (3)        16,000    8,800   7,700  6,500  5,100

Notes:
1. Measurements made in a 29T gallon tank with water only.              
2. Fixture positioned at back of tank and overhung the sides by 9".  
3. Measurements made below center of bulb. 
4. Bulb centerline was 5 cm above water surface.
----------------------------------------------------------------------------

The intensity in water was surpising at first.  From 0 to 10 cm, the 
intensity dropped by half.  Below that, the intensity dropped much
less and linearly with distance.  I speculate that reflections from
the sides of the glass were augmenting the intensity at lower depths
and cannot be depended on in a real setup with plants and all.  When 
I get the 120 gallon tank setup, I will repeat these measurements.  It
is 24" wide and 48" long, which should reduce the reflections. 

"Gentlemen, start your theories"

=============================================================================
George L. Booth                      The Technology of Freshwater Plant Tanks 
booth-at-hplvec.lvld.hp.com             __         Aquatic Gardeners Association
Software Development Engineer       /  \  /\        Colorado Aquarium Society
Manufacturing Test Division      /\/    \/  \         Rainbowfish Study Group
Hewlett-Packard Company         /  \/\  /    \/\         "Modern Aquascaping"
Loveland, Colorado  _____utah__/    \ \/      \ \___me____________kansas_____
=============================================================================

AQUAMYTH #1 More Light for Deep Tanks -- NOT!

by huntley-at-ix.netcom.com (Wright Huntley )
Date: Sat, 21 Oct 1995

This is one of a (proposed) series of posts aimed at exploding (or at 
least questioning) some of the mythology that is frequently repeated 
here.

I'll start in my area of expertise, for I have been involved heavily in 
optical engineering for over 30 years. Your flame opportunities will go 
up dramatically, as I shift to subjects that are not so close to home. 
:-)

If the lamp housing is on, or close to, the top of the tank, the amount 
of light reaching the bottom does not depend on depth.

We aren't talking the Monterey aquarium here, but a tank 1m deep and a 
tank 0.5m deep will have virtually identical illumination at the 
substrate.  Check it out with any light meter, keeping the 
lamp-to-water distance constant, changing only depth.

A distributed source, like fluorescents, couples light into the water. 
with inside-the-tank propagation within what is called the critical 
angle. Light hitting the sides of the tank is totally reflected, for it 
is beyond the critical angle. It is absorbed or reflected by objects in 
the tank, but keeps going until it finds such objects, like a huge 
light pipe.

The situation is only slightly different for a pendant MH hanging well 
above the water, in that the the total light in the tank depends 
greatly (by roughly 1/R^2) on the lamp-to-water distance. Once the 
light is inside the water, however, the propagation is still in a light 
pipe, and only absorption and scatter cause light to be lost. The water 
absorption, at normal aquarium depths, can usually be ignored, unless 
you are horribly addicted to overfeeding. <g> There is a little more 
absorption of the valuable red light in thick-wall glass tanks, but 
this is mostly a secondary effect of concern only in FW tanks.

It would be nice if some of the old-timers would quit advising that 
more light is needed for deeper tanks. In general it isn't. I recognize 
that heavy plant growth absorbs a lot of light, and a really thickly 
planted tank may use some more Watts (NOT lumens, by the way), but 
that's the subject of another missive. The point is that it is 
certainly not the depth that calls for more light.

Wright

More Light for Deep Tanks - NOT!

by nfrank-at-nando.net (Neil Frank)
Date: Sun, 22 Oct 95

Wright, it is not that I did not trust you, but I had to confirm your
statements for myself.:-) After all, there is literature like Kirk's _Light
and Photosynthesis in Aquatic Ecosystems_ that say " downward irradiance
diminishes in an approximately exponential manner with depth."

Since I have a light meter, I put it in a baggy and then made a few
measurements on my two four bulb setups. The numbers in footcandles confirm
your wisdom.

- ----------------------------------------------------------
125 gal. tank - 4 6ft bulbs |  70 gallon tank, 4 4ft bulbs
      a    b    c    d      |  a   b     c    d 
                            |
 Dimpled relector material
 ____v_______v________v___                                ( ) indicates the 
bulb

+6"--( )--( )--( )--( )---|         triton    
     600  880  980 800    |        reflectors           <--fc directly under
bulb 
|                         |    _____      _____ 
                          |   /     \    /     \            
+4"                       +--( )--( )----( )--( )--         
|                         |  800  800    550  500       <--fc directly under
bulb     
|
+3"        600            +              
|                         |
|                         |
+2"                       +   680
|                                                        Water
0~~~ 400~~~480~~~~480~~~~~~~~~~~~~~~~550 <380>~~~~~~~~~~ surface
|                         |
|                         |              
|                         |
- -6"         320 {350}     +           400 <200>
|                         |
|                         |
|                         |
- -12"        300 {350}     +           400 <200>
..                         .
..                         .
..                         .
- ----------------------------------------------------------------
Notes:
6 ft. Bulbs over 125                    4 ft. Bulbs over 70g
 a. spectralite 55w                      a. Triton 40w
 b. daylight HO 85w                      b. Cool white 40w
 c. cool while 55w                       c. Sylv. grow lux WS 40w
 d. grow lux WS 85w                      d. Philips Agro lite 40w
- -----------------------------------------------------------------------------
Numbers in <> brackets show intensity without triton reflectors.
Numbers in {} brackets show intensity with triton reflectors added.
Underwater measurements are approximate, probably +/- 30 fc because meter
was hard for me to read.
- ---------------------------------------------------------------------------

Wow, thanks Wright. I am glad we have an expert onboard. I never took the
time to take the measurements and always thought that the light attenuation
was the same in air and water. Consequently, I did not pay attention to the
additional 2 inches above the water surface in my 125 setup. That explains
why the plants do not grow as rapidly in that tank. My numbers also show the
advantage of using a good reflector, such as the one made by triton. Now I
have to work on lowering those bulbs, instead of adding more of them.

Kirk also notes that says that turbidity can further attenuate the light
(which must be true), and yellow color from organics (gilvin) absorbs blue.
Any comments from the expert?

Neil
Neil Frank   Editor of "The Aquatic Gardener"  Aquatic Gardeners Association
    


Light vs. Depth

by Erik Olson <(e-mail)>
Date: Sun, 22 Oct 1995

> From: huntley-at-ix.netcom.com (Wright Huntley )
> Date: Sat, 21 Oct 1995 14:10:59 -0700
> Subject: AQUAMYTH #1 More Light for Deep Tanks -- NOT!

> This is one of a (proposed) series of posts aimed at exploding (or at 
> least questioning) some of the mythology that is frequently repeated 
> here.
....
> We aren't talking the Monterey aquarium here, but a tank 1m deep and a 
> tank 0.5m deep will have virtually identical illumination at the 
> substrate.  Check it out with any light meter, keeping the 
> lamp-to-water distance constant, changing only depth.
> 
> A distributed source, like fluorescents, couples light into the water. 
> with inside-the-tank propagation within what is called the critical 
> angle. Light hitting the sides of the tank is totally reflected, for it 
> is beyond the critical angle. It is absorbed or reflected by objects in 
> the tank, but keeps going until it finds such objects, like a huge 
> light pipe.

I checked this myself empirically.  The rest of you can do this at home
too. Put your eye close to the front glass of your tank and look up at the
water surface.  Move your head down until you can see the light from
above.  That's where you hit the critical angle, and at depths below this
the light will start to escape through the tank front and back. For my
tanks, this happens at about 18" below the surface.  So while I agree with
Wright's point for tanks of 18" or less depth, I would tend to disagree for
tanks of 20" or more (which is what the old timers are usually cautioning
folks about). 

Another point worth noting is that we don't have perfectly-reflecting 
tank walls here!  There's algae, crud, possible flat black paint, 
etc, which are all helping to ABSORB much of that light instead of 
reflecting it back into the tank.  The deeper the tank, the taller the 
walls, the more surface area potentially covered in crud to eat the light.

(This is certainly a good argument for keeping your tank walls shiny clean 
and algae-free!)

A simpler way of looking at it is that you're trying to distribute all 
the light (wattage) to all 5 walls of the tank (bottom + 4 sides).  As 
the tank gets taller, the total surface area increases and the same light 
must be diluted over this increased area.

Unfortunately, I don't have a light meter, but I think George Booth does. 
In fact, I recall a posting remotely (though not directly) concerned with
this effect... Perhaps he can be coerced into a simple little depth 
experiment? :)

....
> planted tank may use some more Watts (NOT lumens, by the way),

(yeah, but Watts doesn't refer to light output on the bulbs; it refers to 
the consumption, right?)

     - Erik
- ---
Erik D. Olson                                            amazingly, at home
(e-mail)

AQUAMYTH #1 lights in deep tanks

by Stephen.Pushak-at-saudan.HAC.COM
Date: Sun, 22 Oct 95

Wright Huntley wrote:
> Subject: AQUAMYTH #1 More Light for Deep Tanks -- NOT!
> 
> This is one of a (proposed) series of posts aimed at exploding (or at 
> least questioning) some of the mythology that is frequently repeated 
> here.

Good! I always enjoy a nice explosion (as long as it's in good taste! ;-)
>From time to time a too near detonation can send a few bits of our egos
splattering (Doom-style) against the upholstery. Often a little shaking
is exactly what we need and remember, as we pick ourselves up and dust
off the shards of the video display, to take comfort that the scientific
method always involves questioning and we are friends here for a bit of
fun, diversion and learning. I just wanted to say that; no particular
reason. ;-)

> If the lamp housing is on, or close to, the top of the tank, the amount 
> of light reaching the bottom does not depend on depth.

In an tank with only water (no plants or algae), I'll go along with this.
In a tank with some degree of turbidity (lack of clarity) there would be
a diminishing but perhaps not as much as we'd think. As well, the
absorption coefficient of water would depend on the light frequency
as well. Can you give us any data on absorption vs. light color Wright?
I have a feeling you're ready to counter on this point. ;-)

> Light hitting the sides of the tank is totally reflected, for it 
> is beyond the critical angle. 

Another way to illustrate this is to hold a piece of paper near the glass
at the bottom of the aquarium. Hmmm... no light comes from within with
MH pendant ~18" from the water surface of a 28"deep (24"x24" base).
You can exploit this to your advantage by putting a high light plant at
the corners of such a tank where you get good lighting. Those plants
at the centre have the advantage of a considerable reduction in
intensity complements of the much TALLER plants which can surround.
There don't seem to be any distinct shadows even with very large leaves
like E cordifolius. This is due in part to having a diffusion lens in
my pendant as well as a parabolic reflector but also to the refraction/
reflection effect sending light into the "shadowy" parts of the tank!

> The situation is only slightly different for a pendant MH hanging well 
> above the water, in that the the total light in the tank depends 
> greatly (by roughly 1/R^2) on the lamp-to-water distance. Once the 
> light is inside the water, however, the propagation is still in a light 
> pipe, and only absorption and scatter cause light to be lost. 

Where Neil Frank can increase his lighting effectiveness by dropping
his lights, I can diminish mine by raising the lights.  The parabolic
reflector tends to make the dependency not 1/R^2 but I can still spill
lots of light. A proper reflector can do a good job of sending an almost
parallel wide beam of light straight down.

You have a very good point Wright. This particular bit of aquarium lore
is mentioned in The Optimum Aquarium (Horst & Kipper) p143 where
they quote 500-1000 Lux at the surface & 20-30 Lux at the substrate.
I suspect we reinforce some of the misconceptions when we observe the
results in deep vs. shallow tanks where all the factors have to be taken
into consideration. I think H&K must have been talking about a very
wide aquarium (perhaps the 2500g) where the 1/R^2 law is more accurate
due to the lack of close walls to provide reflection!

 Steve


Light attenuation by plants

by nfrank-at-nando.net (Neil Frank)
Date: Sat, 18 Nov 95

The discussion on light penetration and effects of shading are fascinating.
I am grateful to Wright and Charley for 'illuminating' this obscure subject. 

George says
 >>A taller tank DOES need proportionally higher light at the surface if low
foreground plants are too receive enough light.

Clearly, the light changes as it is interrupted by tall plants in our
planted aquaria. But how? Also, do all plants need the same quality (and
intensity) light. Is it possible that plants that like to grow in unshaded
conditions need a different quality light than those that are used to
growing under the canopy of the forest or under other aquatic plants. For
example Glossostigma and Lilaeopsis need more than my chainswords and
crypts. Nevertheless, it would be nice to know what light gets through the
tall and floating plants in our tanks.

The spectral distribution of light changes according to what it passes
through. The Adley book (Dynamic Aquarium) reproduces the figure taken from
Gates (1980) which I attempt to show as a series of ascii drawing below.
[this was my therapy this morning :) ]. Gates' figure highlights the
differences between full sun, cloudy light and light under a tree canopy. I
would love for the experts to comment. With my naive interpretation it seems
that the former two may be appropriate for marine systems and for plants
that like to grow in full sun, while many freshwater plants may be more used
to the latter. 

Several conclusions I draw from this figure are:
 -an artificial light that simulates the sun may not be the most appropriate
for our aquaria.  While some bulbs try to match the red and blue absorption
regions of plants, others try to appeal to our visual appeal. Others may
follow different principles: According to Doug's recent response from ADA,
Amano's fluorescent lights are high in green (From my discussion with him, I
think this is intended to simulate an overcast sky). Dennerle markets their
TROCAL bulb that is intentionally low in blue light (to discourage algae).  
 -there are changes in the light spectrum outside the visible range which
are probably important to plants (especially in the far red region). 
 - there may be similar changes in the quality of light caused by tall
aquatic plants shading others below.

Hopefully these figure will shed some light (and hopefully stimulate further
discussion). I am largely in the dark on this subject. :-)

Taken from Gates (1980)_Biophysical Ecology_ :

                   B  G   Y   R
|...............|.....|.....|...|.........|...........|
0.3            0.4   0.5   0.6  0.7      1.0       10.0
                 Wave length (um)

| -ultraviolet- | -- visible ---|----infrared ----    |
 
                               _  
|                             / |   || |    \
|                           /   | |    |
|                         /      _ | | |     \
|      direct  --->  ___/           || |
|      Sunlight     /               || | | 
|                  /   /\                      \
|                /   /     \           | || | 
|              /    /         \                  \
|             /  -   Cloud light \                 -
|          /                -->     \                \
|      /                               \              -
|../..................................................|


| -ultraviolet- | -- visible ---|----infrared ----    | 
                               _
|                             / | || | 
|                           /   | |   
|                         /      _ |_|      \
|      direct  --->  ___/           || |
|      Sunlight     /               || || 
|                  /    
|                /                  | || | 
|              /                                \
|             /    skylight (shade)
|          /   -------_____                        \
|      /                     -                        
|../..................................................|

| -ultraviolet- | -- visible ---|----infrared ----    | 
                               _
|                             / | || |  
|                           /   | |   
|                         /      _ |_|      \
|      direct  --->  ___/           || |
|      Sunlight     /               || || 
|                  /    
|                /                 ____ 
|              /                  || | |         \
|             /   filtered ---->  |    |            
|          /    thru veget.______ |    |           \-
|      /  __________------             |               
|../....................................\.............|

>From the last drawing, you can see that the spectral distribution of light
changes dramatically as it passes through green foliage. The slope of the
irradiance curve is reasonably linear and is approximately 2 over the
visible spectrum. The blue is reduced more than the long waves, and there is
a significant amount of far red light (.7-.9 um) remaining.

Neil
Visit the Aquatic Gardeners Association home page

Lighting Myths, Revisited!

by Erik Olson
Date: Thu, 31 Oct 1996 07:22:29 -0800 (PST)

> From: JOlson8590-at-aol.com
> 
> Thus far, I have seen no mention of the Law of Inverse Squares as it affects
> lighting.  Very briefly, the intensity of light (any light) shining on a
> surface varies inversely as the square of the distance from the light to the
> surface. This is true, regardless of the efficiency of the reflector, etc.
> (Unless, of course, you have a coherent source of light, such as a laser, but
> they are really lousy lights for growing plants.  :-D  )  

Actually, it ain't necessarily so, specially for us.  Wright Huntley and
others have brought in a lot of interesting discussions on this about a
year ago.

1. The inverse square law only applies to POINT sources of light.  Since
fluorescent fixtures are long skinny things, they're more apt to be
considered "line sources", which drop off light as 1/R (inverse), and if
you've packed a lot of them in, then in the middle of the tank it will
behave as a "plane source", in which there is NO dropoff.  Reflectors will
heavily influence this behavior as they are able to focus light into a
directional beam.  

2. You also have the effect of the side walls, which if clean will reflect
nearly all the light in the tank back into the water due to an effect
called TOTAL INTERNAL REFLECTION.  A little light gets out at the top, but
not much.  This means that in theory almost all the light will stay in the
tank, irregardless of depth!  This only applies to the light once it has
hit the water, so it's ideal (as the original poster said) to position the
source so as much light as possible enters the water, i.e. close to the
surface, or for MH, focused on the surface.

3. On the other hand, you also have other effects that reduce your
intensity:  Plants, Algae, decorations and fish all absorb most of the
light that touches them.  This is sort of a "Duh", but have to mention it,
because it modifies effect 2 to say "get enough light so that it can be
distributed over the countour area of plants"... If you have plants that
grow in a sort of "bowl" shape, up the sides of your tank, you will need
more light than if they are all low-growing on just the bottom part. 

4. Crud in the water (humic acids, unicellular algae, etc) absorbs
light exponentially (intensity = e^ [- (K * depth)].  So for real-life
cases, depth does matter.

    - Erik

---
Erik D. Olson					         amazingly, at home
(e-mail)


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