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/d₀ + 1/dᵢ
Where:
- f is the focal length of the convex mirror
- d₀ is the object distance (distance between the object and the mirror)
- dᵢ is the image distance (distance between the image and the mirror)
Given:
- f = 4 cm
- d₀ = -11 cm (negative sign indicates that the object is in front of the mirror)
Let's substitute the values into the lens equation and solve for dᵢ:
1/4 = 1/-11 + 1/dᵢ
Multiply both sides by 4dᵢ:
dᵢ = 4dᵢ/-11 + 4
Multiply through by -11:
-11dᵢ = 4dᵢ - 44
Combine like terms:
-15dᵢ = -44
Divide both sides by -15:
dᵢ = (-44)/(-15) = 2.93 cm
The image distance, dᵢ, is positive, indicating that the image forms on the opposite side of the mirror as the object. Since the image forms on the same side as the observer looking into the mirror, it is a virtual image.
Therefore, the image will form approximately 2.93 cm behind the convex mirror, and it will be a virtual image.