The fovea in a typical human eye consists of cones which have an average diameter of 1.5 × 10^{-6} m An eye looks directly at two point sources of light which are 12 mm apart at a distance of 61 m from the centre of the eye lens - AQA - A-Level Physics - Question 2 - 2018 - Paper 5

To determine if the eye can resolve the images, we can use the formula for angular resolution:

$heta = 1.22 \frac{\lambda}{D}$

where:

• ( \theta ) is the angular resolution in radians,
• ( \lambda ) is the wavelength of light (approximated to about 550 nm for visible light),
• ( D ) is the diameter of the cones, which is ( 1.5 \times 10^{-6} m ).

Substituting values, we approximate ( \lambda = 550 \times 10^{-9} m ) and ( D = 1.5 \times 10^{-6} m ):

$\theta = 1.22 \frac{550 \times 10^{-9}}{1.5 \times 10^{-6}} \approx 4.46 \times 10^{-1} rad.$

Next, we find the minimum distance that can be resolved based on the distance from the eye lens:

Minimum distance: ( d = 2 \times D \times d_{eye} ) where ( d_{eye} = 61 m ).

Thus:

$d = 2 \times 1.5 \times 10^{-6} \times 61 \geq 3 \times 10^{-6} m \approx 12 \, mm.$

Since 12 mm is larger than the resolution limit, the eye can resolve the two images.