Download The Inverse Square Law The Inverse Square Law

Laboratory#3(b) – Phys4480
Dr. Cristian Bahrim
The Inverse Square Law
Light is a wave phenomenon. The way the irradiance varies with the distance from a real
source of electromagnetic radiation is often complex. However, in some situations we can
consider a point source of light that emits light uniformly in all directions (an isotropic source). In
this case the irradiance is the same in all directions. In this case spherical wavefronts are
spreading out from the isotropic point source.
Let us assume that the energy of the waves is conserved as they spread out from the
point source. At any distance r from the point source, the entire energy emitted by the source is
spread over a spherical wavefront of radius r. Thus, we can say that the rate at which the
energy is transferred through a sphere of radius r by the radiation must equal the rate at which
energy is emitted by the source – that is power Ps of the source. Therefore, the irradiance at a
distance r is given by the formula:
I=
Ps
[1]
4π r 2
Because the same power flows through ever-increasing areas, its concentration per
same area diminishes inversely with the square of the radius. This result is true not only for
electromagnetic waves, but for any mechanical wave produced by a point source. It is the
reason why you cannot read a book by starlight or hear what the players on the field are saying
from up in the stands. Remember that the amplitude of a spherical wave must diminish with the
distance because the energy it carries spreads thinner and thinner as the wavefront gets larger.
In this lab we are going to check eq. [1] using a point source and an ordinary light bulb
as source of light. We assume that all the electric power P = V ⋅ i delivered to the light bulb is
transformed into power radiated, Ps, by the filament. Here V is the voltage across the filament
and i is the current through it. Thus, we consider the heat released by the glowing filament as
being negligible compared with the energy radiated.
Measurements and data analysis:
1. To get the irradiance measured with the photometer in absolute units, we have to do a
calibration. Locate the free end of the optical fiber very close from the source of light.
Don’t put the fiber in contact with the source of light! Put the photometer on a
convenient scale and turn the “Variable Adjust” and “Zero Adjust” knobs until the
photometer reads either 10 or 3 (on the scale). This will be the maximum value for
irradiance, Io, you can measure in this experiment.
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2. Move the free end of the optical fiber along the optical bench at different distances, d.
Start to record data from a distance 1.5 cm. At each distance read the value of the
irradiance read and fill out the table below:
Trial
I(rel.units) d (cm)
1
1.5
2
2.0
3
2.5
4
3.0
5
3.5
6
4.0
7
4.5
8
5.0
9
5.5
10
6.0
11
6.5
12
7.0
13
7.5
14
8.0
15
8.5
16
9.0
17
9.5
18
10.0
19
10.5
Use the inverse square law is: I =
3. Plot Irradiance versus
I(rel.units)
Vi
4π r 2
d (cm)
and has a slope
Vi
.
4π
1
, and check if you find any linear dependence. Understand
r2
the deviation from a straight line when the detector is close to the source of light.
4. If you use the light bulb try to find the slope
Vi
on a spreadsheet. The error analysis
4π
should give you the absolute uncertainty. Record this number and compare with the
theoretical value
Experimental =
Theoretical =
±
If you found a linear trend and in the calculation from above you find agreement theoryexperiment then you discovered that the light travels as a wave!
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