Mr X has mixed astigmatism and has been prescribed a sphero-cylinder glass. In mixed astigmatism ( refer to my video explanation of different types of astigmatism and what is mixed astigmatism https://www.quickguide.org/post/astigmatism-with-toric-iols ) rays of light passing through one meridian (say vertical or 90 degree) falls before the retina and so the rays of light that passes through the horizontal meridan are falling beyond the retina ( Fig 1)
Mr X has been given a prescription of +2 -4 @90 to correct mixed astigmatism. If you have followed my article Understanding Astigmatism or cylinder and how it is corrected by prescription glasses ( https://www.quickguide.org/post/understanding-astigmatism )
you will know why this prescription is prescribed to correct Mr X astigmatism. To be brief the +2 corrects hypermetropia and is placed at 90 degree. The -4 cylinder is the difference of two principal meridians ( one of which is falling before the retina and the other falling beyond the retina). To find the power of the other principal meridain ( at 180 deg) that will correct Mr X mixed astigmatism we will have to do a transposition and add +2 +(-4). Therefore the power at other principal meridian will be -2 which will be placed at 180 deg.
Mr X is unable to adjust to this prescription. The power difference of 4 diopters ( +2 and -2) in two different axis ( 90 and 180 deg) are creating meridional distortaion that his brain is unable to adjust. This is distortion caused by difference in magnification in the two meridians. Thus unequal magnification in different meridians may cause retinal image distortion which some patients may find challenging to accept. Such distortion caused by meridional power difference can lead to binocular spatial difference and therefore may cause problem in depth perception or stereopsis.
The soluction when patients are unable to adjust to their sphero cylinder glass:
Thus modifying the prescription is important.
One way of doing is modifying the sphere and cylinder power while maintaining the spherical equivalent.
Here is the step by step process:
So the initial prescription of Mr X was +2 -4 @ 90 degree. To modify this prescription follow the following steps. It is critical that you do not change the spherical equivalent ( sphere + 1/2 cylinder ) of the prescription.
Step 1 : Calculate the amount of change in spherical power
To get the revised spherical power component of the new prescription to be prescribed the formula is ( old cylinder - new cylinder )/ 2 formula (1)
Let us assume that the new cylinder that the patient is accepting is -1.5 as new cylinder.
Therefore applying formula (1) we get( -4 - ( -1.5)/2) = -2.50 /2 = -1.25
Now we have got the revised sphere from formula (1) as -1.25
Step 2 : Add the revised sphere from formula (1) to the old sphere to get the final sphere
old sphere + revised sphere = New sphere formula (2)
+2 (old sphere) + (-1.25) revised sphere = .75 (New revised sphere)
So the new prescription is +.75 -1.50 @90 degree
To check that you have derived the new prescription correctly, calculate the spherical equivalent of the old and new prescription
Spherical Equivalent = sphere + 1/2 cylinder
Old prescription spherical equivalent is -
+2-4@90 = +2 + (-4/2) = +2 -2 = 0
New presciption equivalent is
+.75 -1.50 @ 90 = +.75 + (-1.50/2) = +.75 +(- .75) = 0