Final answer:
The pupil of a normal adult can gather approximately 13 times more light when it expands from 3 mm in broad daylight to 7 mm in dark conditions.
Step-by-step explanation:
How Much More Light Can the Pupil Gather?
In broad daylight, the pupil size of a normal adult client is typically 3 mm in diameter. In dark conditions, the pupil can expand to about 7 mm. To find out how much more light the expanded pupil can gather, we consider the area of a circle, since the pupil is approximately circular. The area formula for a circle is A = πr^2, where r is the radius of the circle. Thus, when the pupil diameter is 3 mm, its radius is 1.5 mm, and the area (A1) is π(1.5 mm)^2. Similarly, with a 7 mm diameter, the pupil has a radius of 3.5 mm, resulting in an area (A2) of π(3.5 mm)^2.
To determine how much more light can be gathered, we calculate the ratio of the two areas (A2/A1). Simplifying the π term and squaring the radii gives us (3.5^2) / (1.5^2) = 13.3, approximately. This means the pupil can gather roughly 13 times more light when it is dilated to 7 mm compared to when it is 3 mm in diameter.