Where is the Point of Minimal Combined Intensity Between Two Light Bulbs?

  • Context: MHB 
  • Thread starter Thread starter leprofece
  • Start date Start date
  • Tags Tags
    Max
Click For Summary
SUMMARY

The discussion focuses on calculating the point of minimal combined intensity between two light bulbs positioned 16 cm apart, where one bulb has an intensity four times greater than the other. The intensity of illumination is governed by the formula I = k sin(f) / d², where d represents the distance from the source. The solution involves establishing a coordinate system along the line connecting the two bulbs and deriving a function to describe the combined intensity, ultimately leading to the answer of 16/(1 + cubic root of 4) from the more intense bulb.

PREREQUISITES
  • Understanding of light intensity and its inverse square law
  • Familiarity with basic trigonometry and coordinate systems
  • Knowledge of calculus for function minimization
  • Proficiency in manipulating algebraic expressions and equations
NEXT STEPS
  • Study the inverse square law of light intensity in detail
  • Learn about setting up coordinate systems for physics problems
  • Explore calculus techniques for minimizing functions
  • Investigate the application of trigonometric functions in physics
USEFUL FOR

Students and professionals in physics, engineers working with lighting design, and anyone interested in optimizing light intensity in practical applications.

leprofece
Messages
239
Reaction score
0
the intensity of the iluminacibn is directly proportional to the source intensity and inversely proportional to the square of Ia distance to the source. If two light bulbs are 16 cm of distance and one intensity of them is 4 times greater than the other, on which point of the line including Ia combined strength of the two foci is minimal?.

Remenbering
That I = ksin (f)/d2

and sin (h/d)
and d2= r2+h2

How must I organize this?? I tried with two triangles but i did not get the answer
Answer is = to 16/(1+cubic root of 4) from the more intesity bulb
 
Physics news on Phys.org
I would probably begin by orienting a coordinate axis along the line between the two light sources and place the origin at one source. Then, for some point $x$ along the line between the sources, write the function that describes the intensity of light received, and then minimize that function.
 

Similar threads

  • · Replies 1 ·
Replies
1
Views
1K
  • · Replies 10 ·
Replies
10
Views
3K
Replies
3
Views
4K
  • · Replies 2 ·
Replies
2
Views
2K
Replies
1
Views
2K
Replies
1
Views
2K
Replies
5
Views
6K
  • · Replies 152 ·
6
Replies
152
Views
11K
Replies
1
Views
7K
  • · Replies 4 ·
Replies
4
Views
3K