Suppose you are 94 cm from a plane mirror.
Part A
What area of the mirror is used to reflect the rays entering one eye from a point on the tip of your nose if your pupil diameter is 4.8 mm ?
Answer=_______m^2
To calculate the area of the mirror used to reflect the rays entering one eye, we need to consider the size of the virtual image formed by the mirror.
Step 1: Find the distance of the virtual image formed.
Since the mirror is plane, the distance of the virtual image formed is the same as the distance between the mirror and the object.
Distance of virtual image = 94 cm
Step 2: Find the size of the virtual image.
The size of the virtual image can be calculated using the magnification equation:
magnification = size of virtual image / size of object
In this case, the magnification is 1 because plane mirrors create virtual images that are the same size as the object.
Therefore, size of virtual image = size of object
Step 3: Calculate the area of the mirror used to reflect the rays entering one eye.
The area of the mirror used to reflect the rays entering one eye is equal to the area of the virtual image formed.
Area of mirror used = π * (diameter of the virtual image / 2)^2
Given that the pupil diameter is 4.8 mm, we need to convert it to centimeters:
pupil diameter = 4.8 mm = 0.48 cm
Virtual image diameter = 2 * pupil diameter = 2 * 0.48 cm
Now, we can calculate the area of the mirror used:
Area of mirror used = π * (0.48 cm / 2)^2
Area of mirror used = π * (0.24 cm)^2
Area of mirror used ≈ 0.18 cm^2
Therefore, the area of the mirror used to reflect the rays entering one eye from a point on the tip of your nose, when the pupil diameter is 4.8 mm, is approximately 0.18 cm^2.
To calculate the area of the mirror that is used to reflect the rays entering one eye from a point on the tip of your nose, we need to consider the distance between your eye and the mirror, as well as the diameter of your pupil.
Given:
Distance from the mirror = 94 cm
Pupil diameter = 4.8 mm
To start, we need to convert the pupil diameter to meters since the distance from the mirror is given in centimeters.
1 mm = 0.001 m
Therefore, the pupil diameter in meters is:
Pupil diameter = 4.8 mm * 0.001 m/mm = 0.0048 m
Next, we need to find the angular diameter of your pupil as seen from the mirror. This can be calculated using trigonometry.
Angular diameter = 2 * arctan (pupil diameter / (2 * distance from mirror))
Substituting the values for the pupil diameter and distance from the mirror:
Angular diameter = 2 * arctan (0.0048 m / (2 * 0.94 m))
To find the area of the mirror used to reflect the rays entering one eye from the tip of your nose, we need to calculate the portion of the mirror's total area that corresponds to the angular diameter.
The ratio of the reflected area to the total mirror area is given by:
Reflected area ratio = (angular diameter / 360 degrees) * π
Since we only want the area used by one eye, we multiply the reflected area ratio by 0.5.
Finally, we can calculate the area of the mirror used to reflect the rays entering one eye from the tip of your nose by multiplying the reflected area ratio by the total area of the mirror, assuming it is a perfect circle.
Total area of the mirror = π * (radius of the mirror)^2
Now, we can go ahead and do the calculations to get the final answer in square meters.