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I am confused about this problem. This problem confuses me because i dont recall learning anything about this stuff.

You and your friend are trying to heat up your identical fully insulated dinners using desk lamps. You put your food 25 cm from the lamp and your friend puts their food 35 cm away from their lamp. If your food takes 5 minutes to heat up, how long does it take your friend's food to heat up?

Given that the desk lamps can be considered point sources (a fairly decent approximation in this case) the intensity of the emitted light radiation will decrease with the inverse square of the distance. this means that is you double the distance from the light the intensity will decrease to 1/4th of the initial intensity. This means that intensity I is inversely proportional to the square of the distance. Therefore:

I2/I1=R1^2/R2^2f

Using your numbers:

I2=I1*R1^2/R2^2f=I1*25^2/35^2=I1*0.51

Since the intensity at 35 cm is only 0.51=51% of the intensity at 25 cm the time to heat up the TV dinner at 35 cm will take longer. Therefore:

T2=T1/0.51=5min/0.51=9.80min

Physics

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I am teaching or have taught AP physics B and C [calculus based mechanics & electricity and magnetism] as well as Lab Physics for college bound students. I have a BS in Physics from the University of Pittsburgh and a Master of Arts in Teaching from same. I have been teaching physics for 34 years. I am constantly updating my skills and have a particular interest in modern physics topics.