A better approach, especially when dealing with Metal Halide lamps is to size the lamps by the depth of the tank and determine the number of lamps by the square footage of the tank surface.
175W MH is suitable for up to 18” deep tank
250W MH for 18” to 24” deep
400W MH for anything deeper than about 24”
These are ballpark estimates only for a moderate intensity tank. High intensity lighting might make use of 400 watt MH on tanks as shallow as 18".
The other factor is the number of lights and the rule of thumb is that a MH lamp will illuminate approximately a 2’ x 2’ area of the tank. A 4-foot long tank would require 2 MH lamps. This is true whether the tank is 18” wide or 24” wide. A 6 foot long tank would require 3 lamps and an 8 foot long tank would require 4 lamps. If the tank is a more square configuration, the same basic rules apply. A 5-foot long tank that is 36 wide has 15 sq./ft. of surface area. Since each lamp can cover approximately 4 sq./ft., 4 lamps would be the appropriate number to use.
Other major factors that affect the intensity of the light are:
The distance of the light from the surface of the water. The light drops off by the square root of the distance. Lights 4" above the water provide significantly more light into the water than lights 16" above the water. The only things that prevent the lights from being mounted with minimal spacing is heat buildup in the water, possible damage to the lights from water splashes and possible damage to the tank itself if it is made of acrylic or if it has a plastic brace near the lighting that can be damaged from the heat. Oh, and possible damage to your arm when you try to service the tank.
Depth of the water has a significant affect. In any given tank, the lighting will be brightest at the surface of the water and decrease with depth.
Coloration of the water due to dissolved organics can block considerable amounts of light.
A good quality reflector which directs light otherwise lost in the canopy back to the water surface can have a significant affect on the amount of light entering the tank.
Any surface between the light and the water surface will reduce the light intensity, especially if dirt, algae or salt covered.
Lighting Color
The color of the lighting must simulate the sun at some depth in the ocean. Sunlight in shallow water has not been affected much, but as the water deepens, the red and yellows of the light are absorbed while the blues and violet colors stay relatively strong. At 15 feet down on a reef, the light is tinted slightly blue. At 50 feet, the light is strongly blue and the overall intensity is lower.
Color of lighting is typically referred to using the Degrees Kelvin scale. The lower the degrees Kelvin, the more yellow/red the color will be. This is also referred to as a low color temperature. The higher the degrees Kelvin, the bluer the color will be and is referred to as a high color temperature.
We can relate this to our tank in the following manner. The lower color temperature lights simulate a shallow reef, while a higher color temperature light simulates a reef in deeper water. Lighting on the market typically starts out at about 5500 °K. There are even some being sold that have a 4300 °K color temperature. These have more yellow caste to them most people prefer. I recommend that a minimum of a 6500 °K light be used to simulate a shallow reef. These are often supplemented with blue lights called Actinic lights to give a slightly higher color temperature (bluer color). These actinic lights are also useful for simulating low light sunrise and sunset conditions in your reef. Other lights have a rating of 10,000 °K which give a crisp, bluish/white light which simulates a depth of about 15 feet. There are other lights that have a rating of 12,000 to 20,000 K which give a deeper blue light which simulates a fairly deep reef.
In general, there is a tradeoff between the color temperature of the lamp and the intensity of the light it produces. The rule is, the higher the color temperature of the lamp, the lower the intensity of its light output. A 250W 6500K lamp will tend to have more light intensity than a 250W 10K lamp for instance. 10K lamps are the optimal compromise between the look and intensity for many reef tanks. 12K and above are gaining popularity, but frequently have a strong enough blue tint to them that some people do not like them. The intensity is also pretty low.
Another consideration when choosing a metal halide bulb is the CRI (Color Rendition Index) The CRI index relates to how well the light reproduces the true colors of an object. This number ranges from 0-100 with the natural sunlight registering 100. Artificial lighting rarely exceeds 95 and is often lower. Most 10K lamps have a CRI of around 95 and thus do a better job of reproducing the true colors of the coral and other specimens than most other lighting.