Focal Length of a Concave Mirror
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flagWhat you'll discover
- arrow_forwardState the mirror formula 1/f = 1/v + 1/u and use it
- arrow_forwardExplain why parallel rays from a distant object converge at the focus
- arrow_forwardDescribe the image when the object is beyond C, at C, between C and F, and between F and the pole
- arrow_forwardCompute the magnification m = −v/u and say what its sign means
- arrow_forwardFind the focal length of a concave mirror by the distant-object method
The mirror formula
A concave mirror is a piece of a sphere. Its centre of curvature C lies on the principal axis at a distance R from the pole, and the focus F lies halfway between the pole and C, so f = R/2.
For real, positive distances the mirror formula is 1/f = 1/v + 1/u, which rearranges to v = uf/(u − f). Distances are always measured from the pole of the mirror, on the axis. If v comes out positive the image is real and in front of the mirror; if it comes out negative the image is virtual and behind the mirror.
Magnification is m = −v/u. A negative m means the image is inverted relative to the object.
The distant-object method
If the object is very far away — a tree, a building, the sun on a screen — the rays reaching the mirror are effectively parallel. Parallel rays reflect through the focus, so the sharp image forms in the focal plane. That is the quickest way to measure f: hold the mirror facing a distant object, move a screen until the image is sharpest, and the pole-to-screen distance is f.
In the lab you do this three times, average the readings, and also do the u-v method for a check. The two answers should agree to within your reading error.
Image for every object position
Object beyond C: image between F and C, real, inverted, diminished. Object at C: image at C, real, inverted, same size. Object between C and F: image beyond C, real, inverted, magnified. Object at F: image at infinity. Object between F and the pole: image behind the mirror, virtual, erect, magnified.
A dentist's mirror and a shaving mirror both put the face between the pole and the focus, which is why they magnify. A torch reflector puts the bulb at the focus, so the reflected beam is parallel.