How Do You Solve These Basic Illumination Problems?

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To solve the illumination problems, the formula I = L / R^2 is essential, where I is intensity, L is luminous flux, and R is the distance from the light source. For the first problem, the illumination 4.2 m below a 415 lm lamp can be calculated using this formula. In the second problem, to find the distance of the second lamp from the screen, the equal illumination condition must be applied, considering the luminous fluxes of both lamps. The third problem requires calculating the intensity of the second lamp using the same principles of equal illumination and the known intensity of the first lamp. Understanding the inverse square law is crucial for accurately solving these illumination scenarios.
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1) Find the illumination 4.2 m below a 415 lm lamp.

2) A screen is placed between two lamps so that they illuminate the screen equally. The first lamp emits a luminous flux of 1445 lm and is 2.7 m from the screen. What is the distance of the second lamp from the screen if the luminous flux is 2350 lm?

3) Two lamps illuminate a screen equally. The first lamp has an intensity of 101 cd and is 4 m from the screen. The second lamp is 5 m from the screen. What is the intensity of the second lamp?

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These should be very easy. However, I'm doing this for a friend and I don't have his book or any of the formulas. Help me out?
 
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Intensity is proportional to the inverse square of radius.

I = L / R^2, this should help you solve all three of hte above questions, since they are basically the same.
 
I = L / R^2
i = 415/4.2^2
 
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