For a concave mirror

PHYSICS · Multi-part · AP · Physics 2: Algebra-based · Geometric Optics · Geometric Optics

Problem

For a concave mirror, the object distance is

u

and the image distance is

v

(both measured from the pole, following the usual sign convention) while the focal length is

f

. (a) Starting from the mirror equation, derive the relation

(u-f)(v-f)=f^{2}

. (b) Using the result of part (a), show that if the image is formed at the centre of curvature, the linear magnification is

-1

. (c) An object is placed at a distance

1.5f

from the pole of the mirror. Using the relation obtained in part (a), determine the image distance and magnification in terms of

f

and then calculate their numerical values for

f=20\,\text{cm}