Question

A trucker sees the image of a
car passing her truck in her diverging rear-view mirror, whose focal
length is 60.0 cm. If the car is 1.85 high and 6.75 away, what is the
location and height of the image.

1/p + 1/q = 1/f
1/675cm + 1/q = 1/(-60cm)
q=-55.1 cm

M=h'/h M=-q/p
M=-(-55.1cm)/675cm =.0816
h'=(.0816)(185cm)=15.1cm

A microscope contains two converging lenses each having a local length
of 4mm. The objective lens and the eyepiece are separated by 87mm. If a
piece of sand is placed 4.20mm from the objective lens, how far is the
final image from the eyepiece. What is the total magnification of the
system?

1/4.20mm + 1/q = 1/4mm
q=84 mm
M=-q/p = -84mm/ 4.20mm =-20mm

Answer 1

I agree with your first answer.

In the second question, you need to determine how far the viewed sand image appears occurs in front of the eyepiece. Magnifications are dimensionless