W9_parallel_resonance.eps

402 Week 12: Lenses and Mirrors

3

f

1

2

s’

s

image

object

Figure 162: Converging mirror with 2f= 20> s= 15> f= 10.

object

1

3

2

f

image

s

s’

Figure 163: Converging mirror withs= 5< f= 10.

In figure (163) the third and last distinct possibility for a convergingmirror is drawn. In

this case, the object is locatedinsidethe focal length ats= 5 cm (forf= 10 cm). Thus

1 /s′= 1/ 10 − 1 /5 =− 1 /10 ors′=−10 cm. The magnification ism=−(−10)/5 = 2.

The final image isvirtual,erect, andlargerthan the object. This is the common way

converging mirrors are used as “makeup mirrors” that present a magnified image of the

user’s face when viewed from inside their focal length.

We only need to presentonediagram for diverging/convex mirrors, as they all have the

same general diagram independent of the relative size ofsandf. Note that the first and

object 1

2

(^3) image
f
s’
s
Figure 164: Converging mirror withs= 20< f= 10.
second rules are “backwards” compared to converging lenses. A ray parallel to the axis
is deflected so it appears to becoming fromthe far side focal length. A ray headedto
the far side focal length is deflected back parallel to the axis. The central ray is drawn
as before.
We applyas alwaysthe mirror/thin lens formula: 1/s′=− 1 / 10 − 1 /20 =− 3 /20 so