A 2cm high object is placed 3cm in front of a concave mirror. If the image is 5cm high and virtual, what is the focal length of the mirror?
To find the focal length of the concave mirror, we can use the mirror formula:
1/f = 1/v - 1/u
Where:
- f is the focal length of the mirror
- v is the image distance
- u is the object distance
Given:
- The object distance (u) = 3 cm
- The image distance (v) is not given directly, but we can deduce it since the image is virtual. In this case, the image distance is negative (-5 cm).
Using the given values in the mirror formula:
1/f = 1/-5 - 1/3
Now, let's simplify the equation:
1/f = (-3 - 5)/(-15)
1/f = -8/-15
Next, let's take the reciprocal of both sides to solve for f:
f = -15/-8
Simplifying further:
f = 15/8
So, the focal length of the concave mirror is 15/8 cm.