Physics

Physics

Problem

Which expression correctly represents the magnification mm produced by a spherical mirror, in terms of image height hih_i, object height hoh_o, image distance vv and object distance uu (all distances measured from the pole using the Cartesian sign convention)? a) m=hiho=vum=\dfrac{h_i}{h_o}=\dfrac{v}{u} b) m=hiho=−vum=\dfrac{h_i}{h_o}=-\dfrac{v}{u} c) m=hohi=−vum=\dfrac{h_o}{h_i}=-\dfrac{v}{u} d) m=hiho=−uvm=\dfrac{h_i}{h_o}=-\dfrac{u}{v}
Intuitive explanation

Magnification tells you how much a mirror enlarges or shrinks an image compared to the object. The key insight is that magnification is the ratio of image size to object size, but it's also equal to the ratio of image distance to object distance—with a crucial sign flip built in by the Cartesian convention. Since distances can be positive or negative depending on whether they're in front of or behind the mirror, the negative sign ensures magnification correctly captures both size change and image orientation (real vs. virtual).

Intuitive explanation

Magnification tells you how much a mirror enlarges or shrinks an image compared to the object. The key insight is that magnification is the ratio of image size to object size, but it's also equal to the ratio of image distance to object distance—with a crucial sign flip built in by the Cartesian convention. Since distances can be positive or negative depending on whether they're in front of or behind the mirror, the negative sign ensures magnification correctly captures both size change and image orientation (real vs. virtual).

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