A dentist uses a small mirror with a radius of 40 mm to locate a cavity in a patient's tooth. If the mirror is concave and is held 16 mm from the tooth, what is the magnification of the image?
To find the magnification of the image produced by the mirror, we can use the mirror formula:
1/f = 1/v - 1/u
Where:
f = focal length of the mirror
v = image distance from the mirror
u = object distance from the mirror
In this case, the mirror radius is given as 40 mm, which means the focal length (f) is half of the radius:
f = r/2 = 40 mm / 2 = 20 mm
The object distance (u) is given as 16 mm, and we need to find the image distance (v). Plugging these values into the mirror formula, we have:
1/20 = 1/v - 1/16
To simplify, we can find a common denominator:
1/20 = (16 - v) / (16v)
Now, cross-multiplying and rearranging the equation, we have:
16v = (16 - v) * 20
16v = 320 - 20v
Combining like terms, we get:
36v = 320
Dividing both sides by 36, we find:
v = 320 / 36
v ≈ 8.89 mm
Now that we have the image distance (v), we can calculate the magnification (M) using the formula:
M = -v / u
Plugging in the values, we get:
M = -8.89 mm / 16 mm
M ≈ -0.556
Therefore, the magnification of the image is approximately -0.556.