1)A 5.0 cm real object is placed at a distance of 5.0 cm from a concave mirror of focal length 10 cm. Find the size of the image.
di= -10
magnification = |di/do|
magnification = |-10/5.0|
magnification = 2
image size = (object size)*(magnification)
image size = (5.0)*(2)
image size = 10 cm (all of that is from the equation drwls gave me)
2)A rod of length 5.0 cm lies along the axis of a concave mirror of radius of curvature 20 cm. The end of the rod closer to the mirror is 15 cm from the mirror. Find the length of the image of the rod.
20/2
10 cm
Yes on 1, and a quick ray diagram ought to confirm it.
On number 2, find the di for each end of the rod, then the difference is the length. I didn't compute it, but your work indicates you handled it as an image perpendicular to the principal axis, which it is not. I will be happy to critique your work on this.
2)f=10
di=(10)(5)/5-10
di=-10
di=(10)(15)/15-10
di=30
you said the difference is the length, so it would be 30--10 which would be 30+10=40? or 30-10=20? I got confused on that part
Not checking your math, if it is -10 and 30, the distance between those points is 40cm.
To find the length of the image of the rod, you can use the mirror formula:
1/f = 1/v - 1/u
where:
- f is the focal length of the concave mirror
- v is the image distance
- u is the object distance
In this case, the object distance (u) is the distance from the end of the rod closer to the mirror to the mirror itself, which is given as 15 cm. The focal length (f) of the concave mirror is the radius of curvature (R) divided by 2, which is 20 cm / 2 = 10 cm.
Plugging these values into the mirror formula:
1/10 = 1/v - 1/15
To solve for v, we can simplify and rearrange the equation:
1/v = 1/10 + 1/15
1/v = (3 + 2)/30
1/v = 5/30
v = 30/5
v = 6 cm
The image distance (v) is 6 cm. Now, to find the length of the image, you can use the magnification equation:
magnification = -v/u
where the negative sign indicates that the image is inverted.
magnification = -6/15
magnification = -2/5
The magnification is -2/5. To find the length of the image, you multiply the object length by the magnification:
image length = object length * magnification = 5 cm * (-2/5) = -2 cm
The length of the image of the rod is therefore -2 cm, indicating that it is inverted.