Final answer:
The focal length of the mirror is 4.0 cm, and the height of the object is 1.5 cm. The mirror equation and magnification formula are used to calculate these values from the given image distance and height.
Step-by-step explanation:
To find the focal length and height of the object of a mirror that produces a real inverted image which is 3.0 cm high at 4.0 cm from the lens when the object is placed 2.0 cm from the lens, we can use the mirror equation and magnification formula.
The mirror equation is given by:
1/f = 1/do + 1/di
And the magnification (m) is given by:
m = -di/do = hi/
Where:
f is the focal length of the mirror
do is the object distance
di is the image distance
hi is the image height
is the object height
Step 1: Calculate the focal length using the provided distances.
do = 2.0 cm (object distance)
di = -4.0 cm (image distance, negative because the image is real)
Substitute into the mirror equation:
1/f = 1/do + 1/di = 1/2.0 + 1/(-4.0) = 0.5 - 0.25 = 0.25
Therefore, f = 1/0.25 = 4.0 cm
Step 2: Calculate the object height using magnification.
m = -di/do = hi/
hi = 3.0 cm (image height)
Substitute into the magnification formula:
m = -(-4.0)/2.0
m = 2
Then, = hi/m = 3.0 cm / 2 = 1.5 cm
The object height is therefore 1.5 cm and the focal length of the lens is 4.0 cm.