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. The fovea is at the centre of the retina a distance of 21 mm behind the centre of the eye lens. Deduce whether the eye would be able to resolve the two images formed at the fovea.

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The fovea in a typical human eye consists of cones which have an average diameter of 1.5 × 10^{-6} m - AQA - A-Level Physics - Question 2 - 2018 - Paper 5

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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 ... show full transcript

Worked Solution & Example Answer:The fovea in a typical human eye consists of cones which have an average diameter of 1.5 × 10^{-6} m - AQA - A-Level Physics - Question 2 - 2018 - Paper 5

Step 1

Distance Calculation

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Answer

First, we calculate the angular separation between the two light sources:

heta = rac{d}{D} = rac{12 imes 10^{-3}}{61} ext{ radians}

where $d$ is the distance between the light sources and $D$ is the distance from the eye.

Next, we convert angular separation to a linear separation at the retina:

ext{Separation at the fovea} = heta imes ext{distance from eye to the fovea} = rac{12 imes 10^{-3}}{61} imes 21 imes 10^{-3} ext{ m}

Step 2

Resolution Condition

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Answer

Using the average cone diameter (1.5 × 10^{-6} m), we check whether the calculated separation is greater than two cell diameters:

If the linear separation at the fovea is greater than $3 imes 10^{-6} ext{ m}$ (which equals twice the diameter of a cone), then the eye can resolve the images.

If the separation is greater than $3 imes 10^{-6} ext{ m}$ , the eye can resolve the images.

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