A shiny metallic Christmas ball ornament 5.10 cm in diameter is used as a mirror. What is the mirror's focal length? please answer in cm. thanks.
focal length is 5.10/2
2.175
To find the focal length of a mirror, you can use the mirror formula, which is:
1/f = 1/v + 1/u
Where:
- f is the focal length
- v is the image distance (distance from the mirror to the image)
- u is the object distance (distance from the mirror to the object)
In this case, since the Christmas ball ornament is being used as a mirror, the object distance (u) will be equal to the radius of the ornament (R), which is half its diameter. Therefore, u = R = 5.10 cm / 2 = 2.55 cm.
Now, we need to find the image distance (v). To do this, we can use the mirror magnification formula:
m = -v/u
Where m is the magnification.
Since the ornament is being used as a mirror, the magnification is typically -1 (since the image will be inverted). Therefore:
-1 = -v/2.55 cm
Solving for v, we have:
v = 2.55 cm
Now, we can substitute the values of v and u into the mirror formula:
1/f = 1/2.55 + 1/2.55
Simplifying this equation, we get:
1/f = 2/2.55
Now, solving for f:
f = 2.55 / 2 = 1.275 cm
Therefore, the focal length of the Christmas ball ornament used as a mirror is approximately 1.275 cm.