Please show step by step . find where the image is located and the focal length

Question

Please show step by step. find where the image is located and the focal length of the mirror

what i have so far

m = -si/ so = -i /o

1/f = 1/di + 1/do

DIRECTIONS: Work the problem. You must show all work to receive credit, and you must return this sheet. If you have to construct a graph, use the graph paper provided in the laboratory. A student set up a magnetic optical bench with the crossed arrow target at 22.7 cm. When a concave mirror is placed at 65.2 cm, an inverted image that is 3/4 as tall as the object is formed, (a) Where is the image located? (b) What is the focal length of the mirror?

Explanation / Answer

so o is distancebetween mirror and object
o = 65.2-22.7= 42.5

m = -3/4 = -i/o

i = 3/4 o = 3/4*42.5= 31.875 cm

sothat means images is at 65.2-31.875=33.325 cm

b) 1/I + 1/o = 1/f

1/31.875 + 1/42.5 = 1/f

f=18.214 cm

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