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
To find the length of the image of the rod, we can use the magnification formula:
magnification = -(image distance / object distance)
Since the rod lies along the axis of the concave mirror, the object distance (do) is equal to the radius of curvature, which is 20 cm. The image distance (di) can be calculated using the mirror formula:
1/do + 1/di = 1/f
where f is the focal length of the mirror. Let's substitute the values:
1/20 + 1/di = 1/10
Simplifying the equation:
1/di = 1/10 - 1/20 = 2/20 - 1/20 = 1/20
Multiplying both sides by di:
1 = di/20
di = 20 cm
Now we can calculate the magnification:
magnification = -(di/do) = - (20/20) = -1
The negative sign indicates that the image is inverted.
To find the length of the image (image size), we can multiply the magnification by the object size (length of the rod):
image size = magnification * object size = -1 * 5 cm = -5 cm
The negative sign here also indicates that the image is inverted.
Therefore, the length of the image of the rod is 5 cm, but inverted.
To find the length of the image of the rod, we can use the mirror formula and the magnification formula.
First, let's calculate the object distance (do) using the given information. Since the end of the rod closer to the mirror is 15 cm from the mirror, the object distance (do) is 20 cm (radius of curvature) - 15 cm = 5 cm.
Now, we can use the mirror formula (1/f = 1/do + 1/di) to find the image distance (di). The focal length (f) of the concave mirror is -20 cm (negative because it is a concave mirror). Plugging in the values, we get:
1/-20 = 1/5 + 1/di
-1/20 = 1/5 + 1/di
-1/20 - 1/5 = 1/di
(-1 - 4)/20 = 1/di
-5/20 = 1/di
-1/4 = 1/di
Solving for di, we find that the image distance (di) is -4 cm.
Next, we can calculate the magnification (magnification = |di/do|) using the image distance (di) and the object distance (do):
magnification = |-4/5|
magnification = 4/5
Finally, we can calculate the length of the image of the rod using the magnification formula (image length = object length * magnification):
image length = 5 * (4/5)
image length = 4 cm
Therefore, the length of the image of the rod is 4 cm.