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

The final image is located 84 mm from the eyepiece.

The total magnification of the system is -20mm.

To find the location and height of the image in the rear-view mirror scenario, you can use the mirror equation:

1/p + 1/q = 1/f

where p is the object distance, q is the image distance, and f is the focal length of the mirror.

Given that the focal length of the mirror is 60.0 cm and the object (the passing car) is 6.75 m away, you can substitute these values into the equation:

1/675 cm + 1/q = 1/(-60 cm)

Simplifying this equation will give you the value of q, the image distance. In this case, q comes out to be -55.1 cm.

The negative sign indicates that the image formed by the mirror is virtual, meaning it is formed behind the mirror.

To calculate the height of the image (h'), you can use the magnification formula:

M = h'/h

where h is the object height.

Given that the height of the passing car is 1.85 m, you can calculate the height of the image:

M = (-q/p)

Substituting the values of q = -55.1 cm and p = 675 cm, you can calculate M, which comes out to be approximately 0.0816.

Now, calculate the height of the image (h'):

h' = M * h = 0.0816 * 185 cm = 15.1 cm.

Therefore, the location of the image is -55.1 cm behind the mirror, and the height of the image is 15.1 cm.

Let's move on to the next question.

For the microscope scenario, you can use the mirror equation again to find the image distance (q):

1/p + 1/q = 1/f

Given that the focal length of each lens is 4 mm and the object (the sand) is placed 4.20 mm from the objective lens, you can substitute these values into the equation:

1/4.20 mm + 1/q = 1/4 mm

Simplifying this equation will give you the value of q, the image distance. In this case, q comes out to be 84 mm.

Now, to calculate the total magnification of the system, you can use the magnification formula:

M = -q/p

Given that the object distance (p) is the distance between the objective lens and the sand, which is 4.20 mm, and the image distance (q) is 84 mm, you can calculate M, which comes out to be -20.

The negative sign indicates that the image formed by the microscope is inverted.

To find the distance of the final image from the eyepiece, you need to subtract the image distance (q) from the separation between the objective lens and the eyepiece, which is 87 mm:

Distance from eyepiece = 87 mm - 84 mm = 3 mm.

Therefore, the final image is located 3 mm from the eyepiece.

I hope this explanation helps! If you have any further questions, feel free to ask.

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