An object is placed 11 cm in front of a convex mirror of focal length 4 cm. Using the lens equation, find where the image will form and state whether it is a real or virtual image.
To find the location of the image formed by a convex mirror, we can use the lens equation:
1/f = 1/v - 1/u
Where:
f = focal length of the convex mirror (given as 4 cm)
v = image distance
u = object distance (given as 11 cm)
First, let's plug in the given values into the equation:
1/4 = 1/v - 1/11
Now, let's solve for v:
Multiply both sides by 4v:
v = 4v/4 = (4v/11) + 1
Multiply both sides by 11:
11v = 4v + 11
Subtract 4v from both sides:
7v = 11
Divide both sides by 7:
v ≈ 1.57 cm
The image distance (v) is approximately 1.57 cm.
To determine whether the image is real or virtual, we can analyze the image distance (v).
If v is positive, the image is virtual.
If v is negative, the image is real.
In this case, the image distance (v) is positive, so the image formed by the convex mirror is a virtual image.