The area light covers increases exponentially with distance
The total visible light emitted from a light source is measured as a lumen. The amount of lumens emitted from a headlamp is usually clearly marked on the package.
As the distance increases from the light source the area the light illuminates increases exponentially. The area the light covers at one foot would quadruple at 2 feet. At just four feet the light will cover sixteen times the area at 1 foot. This is true for a narrowly focused beam and a wide angle beam.
The illumination over any given area is measured in lux. In general the higher the illumination or lux the easier it is to see. The relative illumination or lux decreases exponentially with distance from the light source. This is because the area of illumination increases exponentially with distance. You will see the illumination or lux decrease by 75% when doubling the distance from the light source.
Lux = Lumen / Area
Lumen = Lux times Area
Recommended Lux Values
You measure illumination of a certain area in lux. 100 lumens of light falling on one square meter is equal to 100 lux. You will require different levels of illumination for different tasks. In general you will need more illumination or lux the more detailed the task becomes. For example, if you are working on detailed drawing work it require 1,000 lux or more. However, if you are navigating a stairway at night it can require just 15 lux. Measuring the lux or the amount of light that falls on a given surface makes it possible to evaluate if there is sufficient light to perform a given task.
Lux Value Measured in the Office
The measured illuminance at the office showed a lux of 233.9. This is a bit low for the illuminance of an office.
Approximate Lux Values for a 100 Lumen Light
In the above chart the approximate illumination area and lux values are shown at various distances from a 100 lumen headlamp. As the distance from the light source increases the area the light illuminates increases exponentially. As the illuminated area increases the illumination or lux decreases exponentially.
You will see the illumination or lux drop 75% every time the distance doubles.
When hiking you need the right illumination for the terrain.
You will need at least 5 lux in illumination to slowly hike at night. If you have more illumination you will be able to hike faster and safer. However, you might experience some trail conditions that require a lot more illumination because of the terrain.
Remember lux is not equal to lumens. Lux equals lumens divided by lighted area. Therefore, the larger the area the light illuminates the lower the lux. You will see a 75% decrease of illumination or lux when the distance from the light source is doubled.
A 100 lumen headlamp that puts out about 1,400 lux one foot away, will put out about 350 lux two feet away. This means when looking about 16 feet away the light will be about 5 lux or the minimum illumination for hiking a groomed trail at night. In most cases you would want to use a more powerful headlamp with 200 lumens or more to hike at night.
It is important to test your headlamp in safe conditions before your hike to see if your headlamp is effective for your personal needs.
Summary
The total visible light emitted from a light source is measured in lumens. You will see this prominently displayed on most headlamp packaging. Generally the higher lumens the better illumination. However, if the headlamp has a very wide beam the illumination at a distance could actually be poor.
What you should focus on is the illumination or lux you need for your desired tasks. If you are planning on hiking at night you will need a headlamp that can provide at least 5 lux at a distance of about 16 feet. However, if you are navigating more difficult terrain or moving fast you will likely need more illumination.
If you select a headlamp that fails to provide the illumination you need be ready to move a bit slower at night.