# Geometric optics question

This question appeared on this site Q17: here

A concave mirror is broken into two parts and these parts are separated by a distance if 1 cm. The focal length of the mirror is 10 cm. Find the location of images(in cm), formed by the 2 parts of the mirror. The object is midway between the two principal axes at a distance of 15 cm from P.

I don't know whether the principal axis of the mirror is parallel to the principal axis of the mirror below. How do we define the principal axis here? what will the location of the image be? thank you.

• Can we assume, unlike your drawing, that the two mirror segments were separated purely in translation? (that is, the "inner" edges at the 1-cm gap have slope infinity). I'm guessing the problem wants you to see that each segment forms an image as would have been formed if the entire mirror had been moved $0.5 cm$ up or down. – Carl Witthoft Nov 22 '14 at 17:47

Assume origin at the center of the mirrors, we can write $$u = -15 \; \text{cm}, \, f = -10 \; \text{cm}$$ which implies $$v = \frac{uf}{u-f} = -30 \; \text{cm}$$
The "height" of the object is $0.5 \; \text{cm}$, and magnification is $$-\frac{v}{u} = -3$$ Thus the images are formed at $$y = \pm 1.5 \; \text{cm} ,\, x = -30 \; \text{cm}$$