Most confusing section of the MCAT for me. Luckily I think I figured it out.
1/o + 1/i = 1/f = 1/p
f = 1/2r
- The sign convention for o is ALWAYS positive for a single lens system … this means, regardless of what side of the lens/mirror it appears on, it will be positive. For a mirror, the object appears on the same side of the eye. For a lens, it appears on the opposite side.
- If the image appears on the same side as the eye, it will be positive
- If the image appears on the opposite side of the eye, it will be negative
- If the focal point appears on the same side as the eye, it will be positive
- If the focal point appears on the opposite side of the eye, it will be negative
Memorize:
Convex lenses converge
- This allows you to derive three other true statements
If convex lenses converge, then…
- Concave lenses diverge
- Convex mirrors diverge
- Concave mirrors converge
Thus, you know the following
Converge: convex lens, concave mirrors
Diverge: concave lens, convex mirrors
Memorize:
Diverging --> upright, virtual (UV)
Converging --> inverted, real (IR)
The mnemonic CIRDUV may help, or remember C comes before D just as IR comes before UV. Remembering IR and UV as infrared and ultraviolet may help.
Memorize:
f is positive for converging
f is negative for diverging
Memorize:
Converging has an EXCEPTION.
Converging --> upright, virtual when object is in the focal point.
Memorize:
m = -i/o = hi/ho
Finally, memorize what myopia and hyperobia are.
In nearsightedness or myopia, the image converges too soon in front of the retina, therefore light needs to be diverged by a lens of some sort onto the retina. What kind of lens will diverge light? Concave lens. Diverging means focal length is negative.
Hyperobia is the opposite. Image appears too far behind retina, thus you need to CONVERGE the image onto the retina. What kind of lens will converge? Convex lens. Converging means focal length is positive.
