A small statue has a height of 3.8 cm and is placed in front of a concave mirror. The image of the statue is inverted, 1.9 cm tall, and located 14 cm away from the mirror. Find the focal length of the mirror.
The image is real (because it is inverted)and the magnification is 1.9/3.8 = 1/2.
The image distance di is half the object distance do. (do = 2 di)
1/di + 1/do = 3/do = 1/f
f = do/3 = 2 di/3 = 9.33 cm
Check:
1/28 + 1/14 = 1/9.33
To find the focal length of the concave mirror, we can use the mirror formula, which is:
1/f = 1/v - 1/u
Where:
- f is the focal length of the mirror
- v is the image distance from the mirror
- u is the object distance from the mirror
In this case, we know that:
- The image distance, v, is given as 14 cm
- The object distance, u, is the height of the statue, which is 3.8 cm. (Since the statue is placed in front of the mirror, the object distance is considered positive)
Now, let's substitute the known values into the mirror formula:
1/f = 1/14 - 1/3.8
To solve for f, we need to find the reciprocal of both sides:
1/f = (3.8 - 14) / (14 * 3.8)
Simplifying the right side of the equation:
1/f = -10.2 / 53.2
Finally, taking the reciprocal of both sides:
f = -53.2 / 10.2
Therefore, the focal length of the concave mirror is approximately -5.22 cm.