CATAGORY: Light
QUESTION: Two light sources on a photometer bench are 90.0 cm apart. One
light source is rated at 20.0 candela. The two sides of the photometer
screen are equally illuminated when the screen is 40.0 cm from this
source.
What is the intensity of the other source?

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For the arrangement in the figure below

 light 1                                           light 2 
 20.0 candela                                      X candela
 
   \|/             screen                             \|/
  - O - -------------|------------------------------ - 0 -                     
   /|\                                                /|\
    |----------------|---------------------------------|
         R1 = 40 cm         R2 = 90cm -40cm = 50cm 
   
            
We have the folllowing.

(1)  flux at the screen ~ L/R^2

Since the fluxes are equal (equal illumination)

(2)     L(1)     L(2)
        ----  =  ----
        R1^2     R2^2
        
thus
                R2^2              (50cm)^2
(3)  L(2) = L(1)---- = 20 candela -------- = 31.25 candela.
                R1^2              (40cm)^2
         
         *************************
         *                       *
         * L(2) = 31.25 candela. *
         *                       *
         *************************