Angular magnification of flat and concave mirrors

[4Phreal]

Homework Statement

(a) I hold a flat mirror 22.4 cm in front of my face. There is a freckle on my
face 1 mm in diameter. Find the angular size of the freckle on the image of my face as
viewed by my eye. (b) Repeat for a concave mirror which has a focal length of 39 cm.
(c) What is the angular magnification of the concave mirror, as compared to the flat
mirror?

Homework Equations

m = θ/θ2
M=h'/h=-q/p
1/p+1/q=1/f

The Attempt at a Solution

For part a: I figured that θ is the angle with the mirror in use, and θ2 is the angle when the object is placed at the nearpoint without the mirror. I assumed I was looking for θ, so I drew a triangle and did the arctan of 0.1cm/44.8cm to get 0.128 degrees as my answer. I'm not sure if that is correct.

For part b: I found q using 1/p+1/q=1/f, and it was -52.62650602 cm. I then calculated total distance, q+p = 52.62650602 cm + 22.4 cm = 75.02650602cm. Then using M=-q/p, i calculated the magnification to be 2.34939759, making h' 2.34939759 mm. Then to find theta, I did arctan(h'/totaldistance) to equal 0.179 degrees. Probably wrong.

Part c: I took angular size from part b and divided it by the angular size in part a because i figured that theta2 is the same for both.

 

[Simon Bridge]

Basically you have tried to remember how to use a bunch of memorized equations - so you are not sure you did it right. Have a go sketching the situation as a way of checking your results using geometry rather than rules.