How to Calculate the Height of an Image Formed by a Concave Mirror
What is the process for calculating the height of an image formed by a concave mirror?
Given an object height of 2.7 cm placed 29.3 cm in front of a concave mirror with a focal length of 11.1 cm, how can we determine the height of the resulting image?
Calculating the Height of the Image
To calculate the height of the image formed by a concave mirror, we need to utilize the mirror formula. The mirror formula is given by: 1/f = 1/v - 1/u
Where:
f = focal length of the mirror
v = image distance from the mirror (positive for real images, negative for virtual images)
u = object distance from the mirror (positive for objects in front of the mirror, negative for objects behind the mirror)
In this case, the values provided are: object distance (u) = 29.3 cm and focal length (f) = 11.1 cm. We first need to calculate the image distance (v) and then use it to determine the height of the image.
Given the formula 1/f = 1/v - 1/u, we rearrange it to solve for the image distance (v):
1/v = 1/f - 1/u
Substituting the given values of u and f, we get:
1/v = 1/11.1 - 1/29.3
Calculating the value of 1/v gives us 1/v = 0.0181. Taking the reciprocal of this value, we find v ≈ 55.25 cm.
Next, we apply the magnification formula to determine the height of the image:
magnification = height of the image / height of the object = -v / u
Substituting the known values, we get -55.25 / 29.3 = height of the image / 2.7. Solving for the height of the image yields approximately -5.10 cm.
Since the height of the image is negative, it indicates that the image is inverted compared to the object.
Therefore, the height of the image formed by the concave mirror is approximately -5.10 cm.