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Inverse Square Law Calculator
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The Inverse law states that the Intensity of waves on any body is inversely proportional to the square of the distance from the source.
I $\alpha$ $\frac{1}{d^{2}}$
If we consider two different distances then Inverse square law is given as:
$\frac{I_{1}}{I_{2}}$ = $\frac{d_{2}^{2}}{d_{1}^{2}}$.
Where I1 is the intensity at distance d1
I2 is the intensity at distance d2.
Inverse law calculator calculates either I1, I2, d1 or d2 if any of the three quantities are given.

Steps for Inverse Square Law Calculator

Step 1 :

Read the problem. Observe the given quantities.

Step 2 :

Use the formula:

$\frac{I_{1}}{I_{2}}$ = $\frac{d_{2}^{2}}{d_{1}^{2}}$

Substitute the given quantities in the above formula to get the desired quantity.

Problems on Inverse Square Law Calculator

1. Calculate the Intensity of light falling at a distance 0.2 m, if the intensity of the same source at distance 0.3 m is 300 candela?

Step 1 :

Given: Intensity I1 = ?

Distance d1 = 0.2 m,

Intensity I2 = 300 candela,

Distance d2 = 0.3 m.

Step 2 :

The Intensity is given by the formula:

$\frac{I_{1}}{I_{2}}$ = $\frac{d_{2}^{2}}{d_{1}^{2}}$

I1 = I2 $\times$ $\frac{d_{2}^{2}}{d_{1}^{2}}$

I1  = 300 $\times$ $\frac{(0.3)^{2}}{(0.2)^{2}}$

= 675 candela.

The Intensity I1 at distance 0.2 m is 675 candela.

2. A Monochromatic light source is producing a intensity of 500 candela and is at a distance of 0.5 m, Calculate its distance if it has a intensity of 700 candela?

Step 1 :

Given: Intensity I1= 500 candela,

Distance d1 = 0.5 m,

Intensity I2 = 700 nm,

Distance d2 = ?

Step 2 :

The Intensity is given by the formula:

$\frac{I_{1}}{I_{2}}$ = $\frac{d_{2}^{2}}{d_{1}^{2}}$

d2 = d12 $\times$ $\frac{I_{1}}{I_{2}}$

d2  = 0.52 $\times$ $\frac{500}{700}$

= 0.4225 m