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The minimum intensity of light that can be detected by unaided human eye is approximately 10 10Wm 2 Estimate the distance at which the Sun could just be seen by unaided eye

Question

The minimum intensity of light that can be detected by unaided human eye is approximately 10 10Wm 2 Estimate the distance at which the Sun could just be seen by unaided eye

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Solution

To solve this problem, we need to use the formula for the intensity of light, which is given by:

I = P / (4πd²)

where:

  • I is the intensity of the light,
  • P is the power of the light source, and
  • d is the distance from the light source.

We know that the minimum intensity of light that can be detected by the unaided human eye is approximately 10^-10 W/m². We also know that the power of the Sun is about 3.8 x 10^26 W.

We can rearrange the formula to solve for d:

d = sqrt(P / (4πI))

Substituting the known values:

d = sqrt((3.8 x 10^26 W) / (4π x 10^-10 W/m²))

Solving this equation gives:

d ≈ 7.3 x 10^16 m

So, the Sun could just be seen by the unaided eye at a distance of approximately 7.3 x 10^16 meters.

This problem has been solved

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