Photographers often use multiple sources of light lightControl the shadows or to enlighten their subject in an artistic way. The lightfrom a light source is inversely proportional to the CarráThe distance from the source and proportional has its intensity. Two Soneof light, Li and L2, are placed 10 m away, and have respectivelyAn intensity of 4 units and 1 unit. Leclairage in any point Pcorresponds to the sum of the lighting from the two sources.An intense light sourceHint: when a quantity is inversely proportional to the square of a, where K is a constant.&nbsp;a) Determine a function which represents the lighting in point P according to itsDistance from point Lb) How much distance is the lighting the most powerful in P?) At what distance from the point is the lighting the weakest in P?d) examine whether it would be more effective to increase the intensity of L2 or to placeL2 closer to Li so as to increase lighting at the point found in C).Press your answer using mathematical evidence. Take into account thetime of lighting and rate of variation in lighting when the intensityor the position of L2 varies.

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Photographers often use multiple sources of light lightControl the shadows or to enlighten their subject in an artistic way. The lightfrom a light source is inversely proportional to the CarráThe distance from the source and proportional has its intensity. Two Soneof light, Li and L2, are placed 10 m away, and have respectivelyAn intensity of 4 units and 1 unit. Leclairage in any point Pcorresponds to the sum of the lighting from the two sources.An intense light sourceHint: when a quantity is inversely proportional to the square of a, where K is a constant.&amp;nbsp;a) Determine a function which represents the lighting in point P according to itsDistance from point Lb) How much distance is the lighting the most powerful in P?) At what distance from the point is the lighting the weakest in P?d) examine whether it would be more effective to increase the intensity of L2 or to placeL2 closer to Li so as to increase lighting at the point found in C).Press your answer using mathematical evidence. Take into account thetime of lighting and rate of variation in lighting when the intensityor the position of L2 varies.

nick1337 · Accepted Answer

a) To determine a function that represents the lighting in point P according to its distance from point L, we can apply the inverse square law for the intensity of light. Let&#039;s denote the distance from point L to point P as x.According to the inverse square law, the intensity of light is inversely proportional to the square of the distance. We can express this relationship mathematically as:I(x)=kx2,where I(x) represents the intensity of light at point P, and k is a constant of proportionality.Since we have two light sources, Li and L2, with respective intensities of 4 units and 1 unit, and they are placed 10 m away, we can find the value of k by substituting the given values into the equation.For Li, we have:4=k102=k100.Simplifying, we find:k=400.For L2, we have:1=k102=k100.Again, simplifying, we find:k=100.Therefore, the function representing the lighting at point P in terms of its distance from point L is:I(x)=400x2 for Li, andI(x)=100x2 for L2.b) To determine the distance at which the lighting is most powerful at point P, we need to find the maximum value of the intensity function I(x).Since both functions are inversely proportional to the square of the distance, their maximum values will occur at the minimum value of x. In this case, the minimum distance is 10 m, which is the distance from the light sources to point P.Therefore, the lighting is most powerful at point P when the distance is 10 m.

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