a thimble is 32.0 cm from a spherical concave mirror. The focal point lenght of the mirror is 11.0 cm. What is the image position?

Answer 1

What you call the "focal point length" is usually called just the "ocal length" with symbol f. it is the place where sources at infinity

Use the formula
1/Do + 1/Di = 1/f
to find the image distance, Di.
The object distance is
Do = 32 cm

1/Di = 1/11 - 1/32 = 21/353
Di = 353/21 = 16.81 cm