Finding Object Distance and Image Distance

[McAfee]

Homework Statement

More mirrors. Object O stands on the central axis of a spherical or plane mirror. For this situation (Table 34-4 below. All distances are in centimeters.) , find (a) the type of mirror (0 depicts "plane", 1 - "concave", 2 - "convex"), (b) the radius of curvature r (nonzero number or 0 if infinity), (c) the object distance p, (d) the image distance i.

f= -42
m= +0.26

(a) 2
(b) -84
(c)
(d)

The Attempt at a Solution

So I'm stuck mainly because the focal length (f) is negative. I think since f is less than m the mirror is convex. Would I still solve for p the same way?

p= (1 - (1/m))*f
so
p= 199.538 cm

and then equals
i = -mp
i = -51.8799

Am I right?

 

[Redbelly98]

There are ways to check your answer to problems like this, which is to see if your solution satisfies the necessary equations.

So: is it true that

1/p + 1/i = 1/f​

or in other words, that

1/199.5 + 1/(-51.9) = 1/(-42)?​

p.s. you're correct that a negative f means that the mirror is convex, and you solve using the usual formula that relates p, i, and f.