Calculus optimization problem?

Click For Summary
SUMMARY

The discussion centers on a calculus optimization problem involving two light bulbs placed 54 feet apart, with intensities of 64 candela (cd) for bulb A and 125 cd for bulb B. The illumination from each bulb varies directly with intensity and inversely with the square of the distance from the source. To find the point along the line between the two bulbs where total illumination is minimized, one must set up an equation for the total illumination as a function of distance and apply optimization techniques to locate the minimum value.

PREREQUISITES
  • Understanding of calculus concepts, particularly optimization techniques.
  • Familiarity with the inverse square law as it applies to light intensity.
  • Knowledge of how to set up and solve equations involving multiple variables.
  • Basic skills in mathematical modeling and function analysis.
NEXT STEPS
  • Study the inverse square law in detail to understand its implications for light intensity.
  • Learn how to derive functions for total illumination based on multiple sources.
  • Practice calculus optimization problems, focusing on finding minima and maxima of functions.
  • Explore numerical methods for solving optimization problems when analytical solutions are complex.
USEFUL FOR

Students studying calculus, physics enthusiasts, and anyone interested in solving optimization problems related to light and intensity.

achiu17
Messages
4
Reaction score
0
The illumination from a bulb varies directly as the intensity of the light and Intensity varies inversely as the square of the distance from the source. Two bulbs are placed 54 feet apart. The intensity, Ia, of bulb A is 64cd, and the intensity, Ib, of bulb B is 125cd. At how many feet from bulb A along the line between the two bulbs is the total illumination the least?

I have no idea how to start this problem...I thought about using optimization but I'm not sure where to start
 
Physics news on Phys.org
If you were dealing with a single bulb, what would the illumination of say bulb A be at a distance x from the bulb?

Similarly, what would the illumination of bulb B be at a distance x?

Assuming that the illumination at a point between the two bulbs A and B is additive, how would you go about finding the point of least illumination?
 

Similar threads

Optimizing Light Pole Height for Maximum Illumination: A Differential Problem
  • · Replies 6 ·
Replies
6
Views
4K
Minimizing Illumination with Two Light Sources on a Parallel Line
  • · Replies 3 ·
Replies
3
Views
4K
Solving for the Height and Width of St. Louis Arch: A Calculus Problem
  • · Replies 4 ·
Replies
4
Views
2K
Where to Place an Object Between Two Light Sources for Least Illumination?
  • · Replies 1 ·
Replies
1
Views
7K
Photon Arrival Rate, Chapter 1.5 from Computer Graphics by Folly
  • · Replies 15 ·
Replies
15
Views
3K
MHB Light Intensity: A & B, Distance D, Minimal Point?
  • · Replies 1 ·
Replies
1
Views
1K
MHB Where is the Point of Minimal Combined Intensity Between Two Light Bulbs?
  • · Replies 1 ·
Replies
1
Views
1K
Undergrad Sound pressure and inverse distance law
  • · Replies 5 ·
Replies
5
Views
3K
Creating a dynamic model for optimization
  • · Replies 12 ·
Replies
12
Views
3K
f(x) = 2x+1, proving that it is continuous when p = 1 with 𝛿 and ε
  • · Replies 7 ·
Replies
7
Views
2K