I will not start here with the history behind Snellen chart, since Dutch ophthalmologist introduced the Snellen chart in 1862. Rather straight to the point, the science behind Snellen Chart.
Why is the Snellen Chart posted at a distance of 6 metres or 20 ft from the patient's eye ? Easy answer for most of us, because at that distance, all rays of light are (assumed) to be entering as parallel rays of light setting at rest the involuntary action of accomodation.
But beyond this the Snellen Chart has more science to it than this simple explanation. It starts with the statement that in order for us to see two things as disctintly separate objects, the angle at which the rays of light should subtend at the nodal point of eye be 1 minute of the arc ( that is 1/60th of a degree ). This is the minimum separable distance that our eye needs to help us to identify two objects distinctively. In terms of the Snellen Chart, what this means is that, each limb of the letter ( say the letter E ) has to be separable by 1 minutes of arc (1/60th of a degree ) subtending at the nodal point of the eye. The nodal point of the eye would be somewhere 17 mm before the retina in model eyes ( with an axial length of 24 mm) or in another way of interpretation, the nodal point of the eye is between the anterior 2/3rd and posterior 1/3rd of the lens. The nodal point is described as the incident ray passing through the front nodal point and emerging through the second nodal point, all leaving at a same angle. That is, though the incoming rays are refracted, yet the outgoing rays from the lens do not change the direction of path from the incoming (Fig 1)
So long we were talking of each limb of the letter 'E' (fig 2). Let us now think of the whole letter ( that is adding all the limbs to form the letter ). So the letters of the Snellen Chart from the top to the bottom, are arranged in such a way, that the entire letter (in this case E) subtends at an angle of 5 minutes of arc at the nodal point of the eye. What this means is that, all the letters in the line depicting 6/6 upto 6/60 should subtend at an anlgle of 5 minutes of arc at the nodal point of eye at their respective distances.
To explain further, if you are sitting in front of the Snellen chart, and record your vision as 6/6, then the letters at 6 metres in that line are subtending at an angle of 5 minutes of arc at the nodal point of eye ( remember each limb of the letter has to subtend 1 minute of the arc ). If you had moved yourself further away to 9 metres, then the letters in the 6/9 line would subtend also at 5 minutes of arc. That is, all the letters of the Snellen Chart from the 6/6 line to the 6/60 line would all subtend at an angle of 5 minutes of arc at the nodal point of eye at their respective 6;9;12;18;24;36;60 meters distances from the chart.
Now the question is, if one is able to read only 6/60, then, what is the minimal angle at which the rays of light has to subtend to help that patient to read ? The answer is simple. If you notice the Snellen Chart, each of the lines are a multiple of 6, except for the line depicting 6/9.
If one is only able to read 6/60 ( as example ) then the minimum angle at which the rays has to subtend at that person's nodal point of eye for each limb of the letter ( E ) can be derived from the Snellen notation, that is in this case the minimum viusal angle should be 10 minutes of arc ( 60/6 ) for each limb of the letter. The person is able to see two points (limbs of the letter ) clearly only when the rays of light are subtending at an angle of 10 minutes of arc at the nodal point of eye.
In terms of the whole letters, this person reading 6/60 is only able to read the letter only when the entire letter ( adding all the limbs of the letter E ) are now subtending at an angle of ( 10 mintues of arc x 5 minutes of arc) 50 minutes of arc. Remember, in terms of the whole letters ( example E ) for a normal person with 6/6 of vision, the rays of light from the top to the bottom of the letter has to subtend at least at an angle of 5 minutes of arc at the nodal point of eye.
Similarly a person who is only able to read 6/18, his minimum angle at which rays of light has to subtend for him to clearly distinguish between two points ( or limbs of letter ) is 3 minutes of arc ( 18/6) at the nodal point of eye. Only then can this person see the two points cearly. In terms of the Snellen chart, this person sitting at 6 metres from the Snellen chart, can read 6/18, because the objects or each limb of the letters are subtending at an angle of 3 minutes at the nodal point of the eye. To see the whole letter (E), his minimum angle of incidence at the nodal point of eye should be then 15 minutes of arc (3 minutes of arch requirement for each of the 5 limbs of the letter E, that is 3 minutes x 5 ).
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