Q.How do you determine the resolving power of your eye?

The resolving power of the eye is limited by diffraction at the pupil; it is quantified by the minimum angular separation (Rayleigh's criterion) at which two point sources can still be seen as distinct, and can be measured experimentally by finding the least separation of two marks that can just be resolved at a known distance.

Theoretical basis: The eye's pupil acts as a circular aperture; light from a point source diffracts as it enters the eye, forming a diffraction (Airy) pattern rather than a perfect point image on the retina. By Rayleigh's criterion, two point objects are just resolved when the central maximum of the diffraction pattern of one falls on the first minimum of the other. The corresponding minimum angle of resolution is

$\Delta\theta = \frac{1.22\lambda}{D}$

where λ is the wavelength of light and D is the diameter of the pupil (aperture).

Experimental determination: Draw two fine parallel lines (or two dots) close together, separated by a small known distance $d$, on a sheet of paper or a wall. Stand far away (distance $x$) so the two marks appear to merge into one, then slowly walk closer until the two marks are just distinguishable as two separate marks. Note this distance $x$. The angle subtended by the two marks at the eye at this point is the minimum angle of resolution of the eye: …

The eye's resolving power is found from the smallest angle at which two nearby points can just be distinguished as separate, set by diffraction at the pupil: Δθ = 1.22λ/D.

Like any optical instrument, the eye's ability to resolve (distinguish as separate) two closely-spaced objects is limited by diffraction of light at its aperture, the pupil. By the Rayleigh criterion, two point sources are just resolved when the central maximum of the diffraction pattern of one falls on the first minimum of the diffraction pattern of the other. The corresponding minimum angular separation is:

Δθ = 1.22 λ/D

where λ is the wavelength of light and D is the diameter of the pupil (aperture).

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The eye's resolving power is determined experimentally by finding the smallest angle subtended at the eye by two closely spaced lines/points that can still be seen as two, rather than merging into one.

Method:

1. Draw two thin, straight, parallel black lines close together (separation $d$) on a white sheet of paper.
2. Fix the sheet on a wall and walk away from it, viewing the lines with one eye, gradually increasing the distance $D$ from the sheet.
3. At some distance, the two lines will just appear to merge into a single thick line — note this distance $D$; this is the point at which the eye can only just resolve (distinguish) the two lines.
4. The angle subtended by the two lines at the eye at this limiting distance is: $\theta = \frac{d}{D} \text{ (in radians, since } \theta \text{ is small)}$ This $\theta$ is the minimum resolvable angle (limit of resolution) of the eye.
5. Resolving power of the eye is defined as the reciprocal of this minimum resolvable angle: $\text{Resolving power} = \frac{1}{\theta}$ …

The eye's resolving power is limited by diffraction at the pupil (Rayleigh's criterion) and can be measured experimentally by finding the smallest angular separation at which two point sources are just seen as distinct.

Resolving power of an optical system (including the eye) is its ability to produce distinguishably separate images of two closely-spaced objects, i.e. to resolve them rather than see them as one blurred point. It is limited fundamentally by diffraction at the aperture (the pupil, for the eye).

Determining it (Rayleigh's criterion): Two point sources are said to be just resolved when the central maximum of the diffraction pattern of one source falls on the first minimum of the diffraction pattern of the other. This gives a minimum angular separation:

$\Delta\theta_{min} = \frac{1.22\,\lambda}{D}$

where $\lambda$ is the wavelength of light and $D$ is the diameter of the aperture (pupil).

Practical/experimental method: Set up two small light sources (or two fine dots on a card) a fixed small distance apart, and view them from a distance that is gradually increased (or decreased). Note the distance at which the two points can just still be seen as separate rather than merging into one — at that point the angle subtended by the two sources at the eye equals the eye's limit of resolution $\Delta\theta_{min}$.

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