Inverse Square Law Problems Solutions
1. The intensity of light from a lamp fixture is 900 millilumens per second, at a distance of 5 metres. What
is the intensity, of this light at 15 metres? 100millilumens / sec
2. The intensity of x-radiation exposing an image receptor is 100 mR at a distance of 25cm. What will the
intensity of radiation be if the image receptor is moved to a distance of 100 cm? 6.25mR
3. The intensity of light from a reading lamp is 500millilumens at a distance of 30 metres. What is the
intensity of this light at a 10.0 metre distance? 4,500millilumens
4. A given technical factor on an x-ray machine will yield an exposure of 160 mR on a radiation meter
which is placed at a distance of 40 inches from the x-ray tube. If the radiation meter is moved to a
distance of 10 inches from the x-ray tube, what exposure will be recorded by the radiation meter?
2,560mR
5. The intensity of radiation from a radioactive source is 900 mR at a distance 20 metres. At what distance
will the intensity of radiation be reduced to 6.25 mR? 240metres
6. A radiographer standing 5 feet from a patient being radiographed on an x-ray table is exposed to 200
mR of scattered radiation. What will the radiographer’s exposure be if she moves to a distance of 15 feet
from the patient? 22.2mR
7. Luminance is a measure of the brightness or intensity of light being emitted from a source such as a
light bulb. Luminance can be measured using a photometer calibrated in the unit nit. At a distance of 9
inches, the luminance of a radiographic viewbox is 1500 nit. What will the luminance be at a distance of
3 inches? 13500 nit
8. At a distance of 100 cm, the exposure from a radioactive substance is measured at 450 mR. What will
the exposure be at a distance of 20 cm? 11250mR
9. A radiologist performing an examination is exposed to 25 mR of scattered radiation standing 3 feet from
the patient. What will be the radiologist’s exposure be if she moves to 12 feet from the patient?
1.5625mR
10. Karen measures the sound intensity at a distance of 5.0 m from a lawn-mower to be 3.0x10-2 W.m-2.
Assuming that the lawn-mower acts as a point sound source and ignoring the effects of reflection and
absorption, what is the total power of the sound emitted by the mower? 9.4 W
11. If the sound intensity 3.0 m from a sound source is 4.0x10-6 W.m-2, what is the intensity at:
(a) 1.5 m from the source? 1.6 × 10−5 W m−2
(b) 12 m from the source? 2.5 × 10−7 W m−2
12. A siren produces a sound intensity level of 90 dB at a distance of 8.0 m. Assume that the siren acts as a
point source of sound.
𝐼
𝑑𝐵 = 10𝑙𝑜𝑔10 (10−12 )
a)
b)
c)
d)
𝑑𝐵
𝐼 = 10( 10 −12) where I is the intensity measured in W.m–2.
What is the sound intensity at a distance of 8.0 m from the siren? 1.0×10–3 W.m–2
What is the power of the sound emitted by the siren? 𝑷 = 𝑰 × 𝑨 = 𝟎. 𝟎𝟎𝟏 × 𝟒 × 𝝅 × 𝟖𝟐 = 𝟎. 𝟖𝟎𝑾
How much sound energy does the siren produce in 1.0 min? 𝑬 = 𝑷 × 𝒕 = 𝟎. 𝟖𝟎𝑾 × 𝟔𝟎𝒔 = 𝟒𝟖. 𝟑𝑱
What is the sound intensity level at a distance of 16 m from the siren? 0.00025 W.m–2 = 84 dB