PtsA flashlight is pointed at the ground, forming a spot of light. The radius of the spot of light is measured and the area of the spot is calculated. The brightness of the spot is measured. Then the flashlight is moved so it is twice as far from the floor. The new brightness will be times the old brightness.

I₂ = I₀  1/4

Explanation:

For this exercise we use the definition of intensity which is the power per unit area

         I = P / A

The emitted power is constant, so

     P = I A

We can write this equation for the start and end point with index 2

    I₀ A₀ = I₂ A₂

    I₂ = I₀ A₀ / A₂

The spot area is the area of the circle

      A₀ = π r₀²

We substitute

     I₂ = I₀ r₀² / r₂²

It indicates that the radius of the spot is twice the initial radius

      r₂ = 2 r₀

      I₂ = I₀ (r₀ / 2 r₀)²

      I₂ = I₀  1/4

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explanation: