4. An object 3.00 cm high is placed 20.0 cm from a convex mirror with a focal length of 8.00 cm.
Find (a) the position of the image, (b) the magnification of the mirror, and (c) the height of the
image
To find the position of the image, magnification, and height of the image formed by a convex mirror, you can use the mirror formula and magnification formula.
(a) The mirror formula relates the object distance (u), the image distance (v), and the focal length (f) of the convex mirror:
1/f = (1/v) - (1/u)
In this case, the object distance (u) is given as 20.0 cm and the focal length (f) is given as 8.00 cm. Plugging these values into the formula, we can solve for the image distance (v).
1/8 = (1/v) - (1/20)
To solve this equation, we can simplify it by multiplying through by the common denominator:
20v - 8v = 20 * 8
12v = 160
v = 160 / 12
v ≈ 13.33 cm
Therefore, the position of the image is approximately 13.33 cm from the convex mirror.
(b) The magnification (m) of a mirror is given by the formula:
m = -v/u
Using the object distance (u) and image distance (v) obtained above, we can calculate the magnification of the convex mirror.
m = -13.33 / 20
m ≈ -0.67
The negative sign indicates that the image formed by a convex mirror is virtual and upright.
(c) The height of the image can be calculated using the magnification formula:
m = -h'/h
Where h' is the height of the image and h is the height of the object.
Rearranging the formula, we get:
h' = -m * h
Since the magnification (m) is -0.67 and the height of the object is given as 3.00 cm, we can calculate the height of the image.
h' = -(-0.67) * 3.00
h' ≈ 2.01 cm
Therefore, the height of the image formed by the convex mirror is approximately 2.01 cm.