Case (i): Object placed between the optical centre and the principal focus of a convex lens

When the object is placed between the optical centre (O) and the principal focus (F) of a convex lens, the ray diagram can be drawn as follows:

1. Draw the principal axis (horizontal line passing through the optical centre O) and mark point O on it.
2. Place the convex lens on the principal axis with its optical centre O aligned with point O on the principal axis.
3. Choose an object AB and place it between O and F.
4. Draw a ray from point A parallel to the principal axis. After refraction, this ray will pass through the principal focus F on the other side of the lens.
5. Draw a ray from point A towards the optical centre O. This ray will pass through the lens undeviated.
6. The ray diagram will show that these two rays after refraction will appear to meet at point A' on the other side of the lens.
7. Mark point A' as the image of point A.
8. Draw a straight line from A' to point B to complete the image AB'.

The image formed is virtual, erect, and magnified.

Sign and value of magnification:
The sign of magnification (m) is positive (+) for virtual and erect images.
The value of magnification can be calculated using the formula:
magnification (m) = image height (h') / object height (h)

Case (ii): Object placed anywhere in front of a concave lens

When the object is placed anywhere in front of a concave lens, the ray diagram can be drawn as follows:

1. Draw the principal axis (horizontal line passing through the optical centre O) and mark point O on it.
2. Place the concave lens on the principal axis with its optical centre O aligned with point O on the principal axis.
3. Choose an object AB and place it anywhere in front of the concave lens.
4. Draw a ray from point A parallel to the principal axis. After refraction, this ray will appear to diverge from the principal focus F on the same side of the lens.
5. Draw a ray from point A towards the optical centre O. This ray will pass through the lens undeviated.
6. The ray diagram will show that these two rays will appear to diverge from each other.
7. Extend the diverging rays behind the lens and trace them back to find the point where they meet. This point will be the virtual image A' of point A.
8. Draw a straight line from A' to point B to complete the image AB'.

The image formed is virtual, erect, and diminished.

Sign and value of magnification:
The sign of magnification (m) is negative (-) for virtual and erect images formed by a concave lens.
The value of magnification can be calculated using the formula:
magnification (m) = image height (h') / object height (h)

Case (iii): Object placed at 2F of a convex lens

When the object is placed at 2F of a convex lens, the ray diagram can be drawn as follows:

1. Draw the principal axis (horizontal line passing through the optical centre O) and mark point O on it.
2. Place the convex lens