Final answer:
To find the radius of a star's image on the retina, use the diffraction limit formula for angular resolution and the distance from pupil to retina. With a pupil diameter of 0.65 cm, wavelength 550 nm, and 2.8 cm to the retina, the radius computes to 2.895x10^-3 cm.
Step-by-step explanation:
To find the radius of a star's image on the retina when the pupil is open to 0.65 cm and the distance from the pupil to the retina is 2.8 cm, we can use the principle of the diffraction limit of a circular aperture. This is described by the formula for the angular resolution, θ = 1.22 λ/D, where λ is the wavelength of light, and D is the diameter of the pupil.
Since the question assumes λ = 550 nm, and pupil diameter D is given as 0.65 cm, we can calculate the angular resolution. However, to find the radius on the retina, we use similar triangles, with the angle found from the angular resolution and the given distance to the retina.
The angle θ in radians is given by:
θ = 1.22 λ/D
θ = 1.22 × 550x10^-9 m / 0.65x10^-2 m
θ = 1.034x10^-4 radians
The linear size of the image is proportional to the distance to the retina, so:
radius = θ × distance to retina
radius = 1.034x10^-4 radians × 2.8 cm
radius = 2.895x10^-3 cm