Convex Lens and Image Formation:

A convex lens is a lens that is thicker in the middle and thinner at the edges. It converges light rays that pass through it and has the ability to form both magnified erect and magnified inverted images of an object placed in front of it.

Ray Diagram for Magnified Erect Image:

To illustrate the formation of a magnified erect image, let's consider an object of height 4 cm placed at a distance of 20 cm from a convex lens. We need to draw a ray diagram to justify this statement.

1. Draw the principal axis: We start by drawing a horizontal line which represents the principal axis. It passes through the center of the lens.

2. Position of the object: Place the object on the principal axis, at a distance of 20 cm from the lens. Label it as "AB".

3. Ray 1 - Parallel ray: Draw a ray from point A parallel to the principal axis. After refraction, this ray passes through the focal point on the opposite side of the lens. Label the refracted ray as "A1B1".

4. Ray 2 - Central ray: Draw a ray from point A towards the center of the lens. This ray continues in a straight line without bending.

5. Ray 3 - Focal ray: Draw a ray from point A towards the focal point on the same side of the lens. After refraction, this ray becomes parallel to the principal axis. Label the refracted ray as "A2B2".

6. Intersection of rays: Extend the refracted rays until they intersect. The point where the rays intersect is the image of point A. Label it as "A'B'".

7. Image formation: Complete the image by connecting point A' and B'. The image is formed upright (erect) and magnified. The height of the image will be greater than the height of the object.

Ray Diagram for Magnified Inverted Image:

Now, let's consider the formation of a magnified inverted image using the same convex lens and object.

1. Draw the principal axis.

2. Position of the object: Place the object on the principal axis, at a distance of 20 cm from the lens. Label it as "AB".

3. Ray 1 - Parallel ray: Draw a ray from point A parallel to the principal axis. After refraction, this ray passes through the focal point on the opposite side of the lens. Label the refracted ray as "A1B1".

4. Ray 2 - Central ray: Draw a ray from point A towards the center of the lens. This ray continues in a straight line without bending.

5. Ray 3 - Focal ray: Draw a ray from point A towards the focal point on the same side of the lens. After refraction, this ray becomes parallel to the principal axis. Label the refracted ray as "A2B2".

6. Intersection of rays: Extend the refracted rays until they intersect. The point where the rays intersect is the image of point A. Label it as "A'B'".

7. Image formation: Complete the image by connecting point A' and B'. The image is formed inverted (upside down) and magnified. The height of the image will be greater than the height of the object.

Position of the Image:

To determine the position of the image formed by the convex lens, we can use the lens