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.

$I \propto \frac{1}{d^2}$

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.

**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. 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.