Inverse Square Law Formula

Inverse Square Law says that the strength of light (intensity) is proportional inversely to the square of the distance.

Inverse Square Law

Inverse Square Law Formula is articulated as

\(I\propto \frac{1}{d^{2}}\)

Where the distance is d, the intensity of the radiation is I.

At distances d1 and d2, I1 and I2 are intensities of light respectively. Then Inverse square law is articulated as:

\(\frac{I_{1}}{I_{2}}\propto \frac{d_{2}^{2}}{d_{1}^{2}}\)

Inverse square law formula is handy in finding distance or intensity of any given radiation. The intensity is articulated in Lumen or candela and distance is given in meters. It has widespread applications in problems grounded on light.

Inverse Square Law Solved Examples

Underneath are some problems based on an inverse square law which may be useful for you.

Problem 1: The intensity of a monochromatic light are in the ratio 16:1. Calculate the second distance if the first distance is 6m?



I1 : I2 = 16 : 1,

d1 = 6m,

d2 =?

Distance, \(d_{2}=\sqrt{\frac{I_{1d_{1}^{2}}}{I_{2}}}\) \(\frac{16\times 6}{1}\) = 9.8m


Problem  2: Compute the intensity of radioactive source antimony 124 if it has the intensity of 80 milliroentgen/hour for 50 feet. At 10 foot, what will be its intensity?



I1 = 80 milliroentgens/hour,
d1 = 50 feet,
I2 =?
d2 = 10 feet.

Intensity, \(I_{2}=\sqrt{\frac{I_{1d_{1}^{2}}}{d_{2}}}\)

= \(\frac{80\times 50^{2}}{10^{2}}\)

= 40 milliroentgens/hour

Practise This Question

Repeated observations in an experiment gave the values 1.29, 1.33, 1.34, 1.35, 1.32,1.36, 1.30 and 1.33. Find the relative error. 

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