What is the relationship between the object distance and the image distance for a convex lens?

The relationship between the object distance and the image distance for a convex lens can be determined using the lens formula. The lens formula states that:

1/f = 1/v - 1/u

Where:

• f is the focal length of the lens
• v is the image distance (distance between the lens and the image)
• u is the object distance (distance between the lens and the object)

In the case of a convex lens, the focal length is positive.

When the object is placed beyond the focal point (u > f), the image distance (v) will be positive and the image will be formed on the opposite side of the lens. The image will be real, inverted, and diminished in size.

When the object is placed at the focal point (u = f), the image distance (v) will be infinite. The image will be formed at infinity and will be real, inverted, and highly magnified.

When the object is placed between the focal point and the lens (f > u > 0), the image distance (v) will be negative. The image will be formed on the same side as the object, it will be virtual, upright, and magnified.

It is important to note that as the object distance (u) approaches zero, the image distance (v) will approach negative infinity. This means that the image will be formed at the same side as the object, it will be virtual, upright, and highly magnified.

In summary, the relationship between the object distance and the image distance for a convex lens depends on the position of the object relative to the focal point.