The amount of light the eye can gather is proportional to the area of the pupil. The area of a circle (which the pupil is) is given by the formula πr², where r is the radius of the circle.

1. First, we need to find the area of the pupil in both situations.

In broad daylight, the diameter of the pupil is 3 mm, so the radius is 1.5 mm. The area is then π*(1.5 mm)² = 7.07 mm².

In dark situations, the diameter of the pupil is 7 mm, so the radius is 3.5 mm. The area is then π*(3.5 mm)² = 38.48 mm².

2. Now, we can find out how much more light the eye can gather in dark situations compared to broad daylight.

The ratio of the two areas is 38.48 mm² / 7.07 mm² = 5.44.

So, the eye can gather about 5.44 times more light in dark situations than in broad daylight.

Question

The amount of light the eye can gather is proportional to the area of the pupil. The area of a circle (which the pupil is) is given by the formula πr², where r is the radius of the circle.

1. First, we need to find the area of the pupil in both situations.

In broad daylight, the diameter of the pupil is 3 mm, so the radius is 1.5 mm. The area is then π*(1.5 mm)² = 7.07 mm².

In dark situations, the diameter of the pupil is 7 mm, so the radius is 3.5 mm. The area is then π*(3.5 mm)² = 38.48 mm².

2. Now, we can find out how much more light the eye can gather in dark situations compared to broad daylight.

The ratio of the two areas is 38.48 mm² / 7.07 mm² = 5.44.

So, the eye can gather about 5.44 times more light in dark situations than in broad daylight.

Knowee AI · Accepted Answer

The amount of light the eye can gather is proportional to the area of the pupil. The area of a circle (which the pupil is) is given by the formula πr², where r is the radius of the circle.

1. First, we need to find the area of the pupil in both situations.

In broad daylight, the diameter of the pupil is 3 mm, so the radius is 1.5 mm. The area is then π*(1.5 mm)² = 7.07 mm².

In dark situations, the diameter of the pupil is 7 mm, so the radius is 3.5 mm. The area is then π*(3.5 mm)² = 38.48 mm².

2. Now, we can find out how much more light the eye can gather in dark situations compared to broad daylight.

The ratio of the two areas is 38.48 mm² / 7.07 mm² = 5.44.

So, the eye can gather about 5.44 times more light in dark situations than in broad daylight.

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?

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