When a torch is brought 2 times closer, how many times brighter will it appear?
2
4
9
16
At first, I figured the answer would be the obvious (2), but then I second-guessed myself and figured 4
I think the answer is 4. The brightness is a function of the distance squared.
To calculate how many times brighter a torch will appear when it is brought 2 times closer, you can use the inverse square law of light, which states that the intensity of light is inversely proportional to the square of the distance.
Let's assume that the original distance between the torch and the observer is d. When the torch is brought 2 times closer, the new distance becomes d/2.
According to the inverse square law, the intensity of light is proportional to the inverse of the square of the distance. Therefore, the ratio of the original intensity to the new intensity can be expressed as:
(original intensity) / (new intensity) = (d^2) / ((d/2)^2)
Simplifying the equation:
(original intensity) / (new intensity) = d^2 / (d^2 / 4)
(original intensity) / (new intensity) = 4
This means that the torch will appear 4 times brighter when it is brought 2 times closer.
So, the correct answer is 4.