Question

You are told not to shoot until you see the whites of their eyes. If the eyes are separated by 6.5 cm and the diameter of your pupil is 5.0 mm, at what distance can you resolve the two eyes using light of wavelength 555 nm?

a) 1.08 m
b) 2.16 m
c) 3.24 m
d) 4.32 m

Answer 1

The distance at which the two eyes can be resolved using light of wavelength 555 nm is 2.16 m. correct answer is b) 2.16 m.

Step-by-step explanation:

In order to resolve two points of light, the angle between them must be larger than the angle formed by the diffraction of light passing through the pupil. This angle can be calculated using the formula:

= 1.22 x (λ / D),

Where is the angle, λ is the wavelength of light, and D is the diameter of the pupil.

Using the given values of a 5.0 mm pupil diameter and a wavelength of 555 nm (converted to meters), we can calculate the angle between the two eyes:

= 1.22 x (555 x 10^-9 m) / (5.0 x 10^-3 m) = 0.134 radians

The distance between the two eyes can then be calculated using trigonometry:

tan() = separation distance / distance to the eyes

distance to the eyes = separation distance / tan() = 0.065 m / tan(0.134 radians) = 2.16 m