The Power of Eyeglasses: A Return to School

School started yesterday. It was the end of a long, long holiday--the longest holiday ever in my recorded history (That is, in my school. Bet some of you could have a whole month off). It was already filled with fascinating new physics equations, fascinating new chemical equations, and fascinating new talks about how our bones are made.

Doesn't new knowledge and ridiculously challenging tests sound entertaining?

No. No sarcasm there.

That holiday's end does mean several new stacks of homework. However, we did have a class Christmas party today. Then, we cleaned the hallways: something that never happened in the school. Quite hard work being those office boys and girls. Thank you kindly.

That said, the first week won't be too depressing, I think. I've still time to watch several stuff (which I may write a review for here), and play Life is Strange (discussions may be coming). So, I also have time to write here. 

Let's get on to the school spirit with this post, shall we? Didn't lie when I said I like school.

Now, I went to the opthalmologist (eye doctor; please, somebody out there should also know) around a month ago, and got my verdict: Minus 6.5 on my right eye, and 4.5 on the left. Quite impressive. Well, to be expected as my eyes have been worsening since first grade, or perhaps technically since two or three, when I started drawing, with my eyes just several centimeters from the paper.

Quite a severe nearsightedness.

About nearsightedness or myopia, it is when your lenses focus light before the retina, thus the images we view become blurry. To correct it, we myopians use concave eyeglasses.

Image taken from commons.wikimedia.org

But those eyeglasses are quite costly, are they not? Moreover, we also need to pay the doctors to check how bad our eyes really are.

Let's cut costs, eh?

The thing to understand is that our eyes has a far point, the farthest point an object is we can focus with our eye accomodation (that is, muscles reshaping the lens). The more often we see stuff that are near to us, the closer that far point becomes.

Please forgive the hastily drawn figure.

On a normal eye, that far point is at infinite distance from our eyes. A myopic eye will have a reduced far point, let's say, x. So all the concave lens needs to do is to put the image of an object at infinity to x, where the eye could see it.

We could use the formula for lens focus length, already learned in junior high physics:

Where f is focus, So is object distance from lens, and Si is image distance. Power of lens, which we want for our eyeglasses, is 1/f. We could also input a number to the variables.

The object is at infinite, and we would want to get the image at the myopic far point at x (in meters). The image distance is negative because it is in the same side of the lens. Then:

One divided by infinity is darn close to zero, so we can ignore it. For convenience, we could use centimeters for x if we make the numerator 100.

There we go. Let's test by preparing something to read off and a ruler. Close one of your eyes, and move the image or text closer to your eyes until it becomes clear enough. Measure its distance from your eyes. Then use that final equation. That'll be the lens you need for the eye.

For example, my right eye could see clearly at 15.5 cm: very poor sight. If we use that equation, we arrive at around -6.5 lens power. Not too much different from what doctor said.

So, shall we make the doctors go bankrupt?

Well, no. I also have astigmatism, where my cornea is misshapen, making the light rays blurred before it hits the lens. Then, that equation will not work for farsightedness--there is another equation, however it is quite faulty, and I haven't looked it through and through just yet. Only doctors would be able to handle those cases.

So, we won't cut costs anytime soon, eh? And more, with the coming of school, there'll be countless sleepless nights (not really, since Dad shall scream when I stay up past nine) which will further degrade my eyes.

Sad. Well, that's all for this time's useless fact.

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References

Wikipedia, which is actually not a proper source. Also my physics notebook, also not a proper source.