In an experiment to find the focal length of a concave mirror, the magnitudes of the object distance u and of the image distance v are measured and a graph of v against u is drawn. The graph looks like .

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(3) (3). Given: a concave mirror with a real object and a real image, so u and v are both measured as positive magnitudes. Idea: in magnitudes the mirror formula is 1/u+1/v=1/f. Rearranged, v=(uf)/(u-f). As u→ f from above, v→∞; as u→∞, v→ f; and the curve passes through u=v=2f. So it is a rectangular hyperbola that never touches either axis, with the lines u=f and v=f as its asymptotes. That is panel (3). A straight line is ruled out at once, because (dv)/(du)=-(v²)/(u²) is different at every point of the curve.

In an experiment to find the focal length of a concave mirror, the magnitudes of the object distance u and of the image distance v are measured and a graph of v against u is drawn. The graph looks like ________.

Step-by-step solution

Why the other options are wrong