Focal Length of Mirrors & Lenses
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flagWhat you'll discover
- arrow_forwardApply the mirror/lens formula through the u-v method
- arrow_forwardRemove parallax to locate a real image precisely
- arrow_forwardCompute f = uv/(u + v) and average over several pairs
- arrow_forwardInterpret the straight-line 1/v vs 1/u graph and its intercepts
The u-v method
For a concave mirror or convex lens forming a real image, object distance u and image distance v obey 1/f = 1/u + 1/v (using positive magnitudes for real objects and images). Measure several (u, v) pairs and each yields f = uv/(u + v); their mean is your result.
Even better is the graph: plotting 1/v against 1/u gives a straight line of slope −1 whose intercepts on both axes equal 1/f. A quick rough start: aim the mirror at a distant window — parallel rays converge at the focus, giving an approximate f so you know where to place pins.
Parallax: how you "see" an invisible image
A real aerial image floats in space with nothing on it to look at directly — so we use parallax. Place the image pin roughly where the image seems to be and move your eye side to side: if pin and image shift relative to each other, they are at different distances. Adjust the pin until they stay locked together from every angle: no parallax, and the pin tip now stands exactly at the image.
Keep all pin tips, the lens centre (optical centre) and the mirror pole at the same height on the bench axis. Note also the index correction: the pin’s position is read from the bench scale, but distances should be measured to the lens/mirror surface — subtract holder offsets.
Choosing distances and avoiding bad data
Place the object BEYOND the focus, or no real image exists — inside f the image becomes virtual, upright and unreachable by the image pin. Avoid u ≈ f (image races off the bench, huge and dim) and u ≈ v ≈ 2f only as one of several points (it is the symmetric case where the image is the same size as the object).
Spread your u values from just beyond f out to about 3f for a well-conditioned graph. Error sources: parallax judged carelessly, bench scale misread, thick lens treated as thin, and the pin not at the principal axis height. Quote f to a sensible precision (0.1 cm) with the mean and the graph value side by side.