A concave mirror forms a real image at 17.0 cm from the mirror surface along the principal axis. If the corresponding object is at a distance of 36.0 cm, what is the mirror's focal length?
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To find the mirror's focal length, we can use the mirror formula:
1/f = 1/v - 1/u
Where:
- f is the focal length
- v is the distance of the image from the mirror's surface
- u is the distance of the object from the mirror's surface
In this case, we are given:
- v = 17.0 cm
- u = 36.0 cm
Plugging these values into the formula, we get:
1/f = 1/17 - 1/36
Now, we can solve for f by finding the reciprocal of both sides:
f = 1 / (1/17 - 1/36)
Simplifying this expression by finding the common denominator (612), we get:
f = 1 / ((36 - 17) / 612)
f = 1 / (19 / 612)
Finally, dividing 1 by (19 / 612), we can calculate f:
f ≈ 32.2 cm
Therefore, the focal length of the concave mirror is approximately 32.2 cm.