Question

In broad daylight, the size of your pupil is typically 3 mm. In dark situations, it expands to about 7 mm. How much more light can it gather?

Answer 1

Answer:

31.4 mm²

Explanation:

Light gathering power of any telescope or eye can be defined by the formula,

$GDP=\pi } \frac{d^{2} }{4}$

Here, d is the diameter of the pupil.

Now for bright daylight the typical size or diameter of the pupil is 3 mm.

$GDP_{b} =\pi \frac{3^{2} }{4}$

Now for dark situation the typical size or diameter of the pupil is 7 mm.

$GDP_{b} =\pi \frac{7^{2} }{4}$

Increase in light gathering power.

$Increase=\pi \frac{49}{4} -\pi \frac{9}{4} \\Increase=31.4 mm^{2}$

Therefore the more light which can gather by eye is 31.4 mm² .