A candle, 3.5 cm high, placed 29 cm in front of a curved mirror forms an image at a distance of 12 cm from the mirror.
Focal length of mirror?
How high is the image?
What type of mirror is this?
To find the focal length of the mirror, we can use the mirror formula:
1/f = 1/d₀ + 1/di
Where f is the focal length of the mirror, d₀ is the object distance, and di is the image distance.
In this case, the object distance (d₀) is the distance from the object (candle) to the mirror, which is given as 29 cm.
The image distance (di) is the distance from the mirror to the image formed, which is given as 12 cm.
Substituting the given values into the formula:
1/f = 1/29 + 1/12
To solve for f, we can take the reciprocal of both sides:
f = 1 / (1/29 + 1/12)
f ≈ 8.694 cm
Therefore, the focal length of the mirror is approximately 8.694 cm.
To find the height of the image, we can use the magnification formula:
Magnification (M) = -di / d₀
The negative sign indicates that the image is inverted.
Substituting the given values:
M = -12 / 29
M ≈ -0.414
The magnification, in this case, is approximately -0.414.
The height of the image (hi) can be determined by multiplying the height of the object (ho) by the magnification:
hi = ho * M
The height of the object is given as 3.5 cm:
hi = 3.5 * -0.414
hi ≈ -1.449 cm
The negative sign indicates that the image is inverted, and the height is approximately 1.449 cm.
Based on the information given, the image formed by the curved mirror is inverted, and its height is smaller than the height of the object. This indicates that the mirror is a concave mirror.