focal point of the eye

[theonlytycrane]

I was initially interpreting this as the retina, but the retina is the point where light rays intersect. And the focal length is adjusted to focus the light rays onto the retina. Am I thinking about this correctly?

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[betterfuture]

Isn't the focal length measured as half the radius of a sphere, so like from the point of half the radius and out? And since the eye has the lens, which is a convex lens, the focal point would be located after the light rays enter the eye, hit the lens and then converge at the focal point. So I would have thought it as the retina too. So it's not?

 

[NextStepTutor_3]

With regard to the human eye, you guys are typically correct! Think of this mathematically (which tends to be easier for optics / lens problems). The focal length of a typical human eye is around 2 cm.

Now, let's say I'm looking at an object that is 20 m away (2000 cm). If we plug into our trusty lens equation (1/f = 1/i + 1/o), we get (1 / 2 cm) = (1 / i) + (1 / 2000 cm). We certainly could calculate this out exactly, but 1/2000 is an extremely small number. This relates to what many passages call a "distant object," which is an object so far away that the "1/o" term can be approximated as 0. For the human eye and its fairly tiny focal length, many (if not most) objects that we look at can be considered "distant."

Now that we've estimated 1/2000 cm to be approximately 0, we get the equation 1/ 2 cm = 1/i, or 1/f = 1/i. This simplifies to f = i. As we certainly want our image to appear on the retina, this equation tells us that the focal length can also be approximated as the distance from the lens to the retina (in other words, equal to the image distance).

Is this always correct? Not exactly - for one, if you're dealing with lenses other than the eye, the focal length may be very large. So there's no guarantee that the object distance will be significantly larger, and we likely have to proceed with the full calculations. Additionally, always keep in mind the conditions that prevent even the image itself from appearing on the retina: hyperopia (farsightedness) and myopia (nearsightedness).

 

[theonlytycrane]

@NextStepTutor_3 the retina is about 2 cm away from the lens in most humans, but can we interpret that as the focal length itself? Since this is where the light rays converge isn't this the image distance?

I guess if we still use o = 20m = 2000cm, we still approximate that f = i and see that the focal length is the same as the image for far objects. Is my initial interpretation correct?

 

[BerkReviewTeach]

For MCAT purposes, it is best (and easiest) to consider the image forming at a point where the rays intersect at the fovea. The reality is that for an inverted, real image to form at the retina, the focal point is ever-so-slightly before the fovea, but we're talking less than a mm. So for simplicity on the MCAT, treat the retina as the focal point.