Lenses
A short lesson with diagrams, a worked example, a problem to try, and a quick check. Then quiz yourself on 6 practice questions.
A converging lens (thicker in the middle) bends light toward a focus: f > 0. A diverging lens (thinner in the middle) spreads it: f < 0. Lenses use the same equations as mirrors, but a real image forms on the far side of the lens.
1. Ray diagrams
2. What a converging lens does
As an object moves in toward F, its real image moves farther away and gets bigger.
Covering half the lens doesn’t cut off half the image: every part of the lens focuses light from every part of the object, so the whole image still forms, just dimmer.
3. Example, then try it
An object is 18 cm from a converging lens with f = 12 cm. Find the image.
1/si = 1/12 − 1/18 = 1/36, so si = 36 cm on the far side: real.
M = −36/18 = −2: inverted and twice as tall.
An object is 30 cm from a diverging lens with f = −15 cm. Describe the image. Then a converging lens with f = 8.0 cm is held 6.0 cm from a stamp. Describe that image.
Diverging lens: 1/si = 1/(−15) − 1/30 = −3/30, so si = −10 cm: virtual, on the object’s side.
Magnification: M = −(−10)/30 = +1/3: upright and one-third the size.
Magnifying glass: 1/si = 1/8.0 − 1/6.0 = −1/24, so si = −24 cm: virtual.
Magnification: M = −(−24)/6.0 = +4: upright and 4 times as large.
Answer: diverging: virtual, upright, ⅓ size; magnifier: virtual, upright, 4×.
4. Common mistakes
An object starts far from a converging lens and moves toward its focal point. What happens to the real image?
As so shrinks toward f, 1/si = 1/f − 1/so shrinks, so si grows, and M = −si/so grows too.
Ready to practice?
6 questions on Lenses, each with a hint and an explanation for every wrong answer.