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Inverse Square Law Calculator

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This Law states that the from the point source, the intensity of radiation is inversely proportional to the square of the distance. Mathematically,
$I \propto \frac{1}{d^2}$

where,
I = intensity of radiation in candela
d = distance in meters

If there are two intensity of radiations $I_1$ and $I_2$ from two distances $d_1$ and $d_2$, then the inverse square law is given as,
$\frac{I_1}{I_2} \propto \frac{d_{2}^{2}}{d_{1}^{2}}$

This online inverse square law calculator help finding the intensity or the distance of any given radiation.

Steps

Step 1 : Note down the values of the given parameter in the question.

Step 2 : Plug in the values into the inverse square law formula i.e.,
$\frac{I_1}{I_2} = \frac{d_{2}^{2}}{d_{1}^{2}}$

and get the desired parameter.

Problems

Based on inverse square law, some of the problems are given below.

Solved Examples

Question 1: The light intensity of a lamp is 800 Candela at a distance of 4 meters. Calculate the light intensity at 16 meters.
Solution:

Step 1 : Given :
$I_1$ = 800 Candela
$I_2$ = ?
$d_1$ = 4 meters
$d_2$ = 16 meters

Step 2 : Substituting these values into inverse square law formula,
$\frac{I_1}{I_2} = \frac{d_{2}^{2}}{d_{1}^{2}}$

$I_2$ = $\frac{d_{1}^{2} \times I_1}{d_{2}^{2}}$

$I_2$ = $\frac{(4)^{2} \times 800}{(16)^{2}}$

$I_2$ = 50

Therefore, the light intensity of lamp is 50 Candela.

Question 2: At a distance of 15 meters, the intensity of radiation of a radioative source is 500 Candela. At what distance, the intensity of radiation is reduced to 7 Candela?
Solution:

Step 1 : Given :
$I_1$ = 500 Candela
$I_2$ = 7 Candela
$d_1$ = 15 meters
$d_2$ = ?

Step 2 : Substituting these values into inverse square law formula,
$\frac{I_1}{I_2} = \frac{d_{2}^{2}}{d_{1}^{2}}$

$d_{2}^{2}$ = $\frac{d_{1}^{2} \times I_1}{I_2}$

$d_{2}^{2}$ = $\frac{(15)^{2} \times 500}{7}$

$d_{2}^{2}$ = 126.77 meters

Therefore, the distance is 126.77 meters.