A negative focal length indicates that the lens is a diverging lens. Given that, we'll draw the ray diagram accordingly.
Ray diagrams for diverging lenses follow these rules:
1. A ray parallel to the principal axis will appear to diverge from the focal point on the same side of the lens as the object after passing through the lens.
2. A ray passing through the center of the lens will continue undeviated.
Let's proceed to draw the ray diagram. You'll need graph paper, a ruler, and a pencil. Here's how to proceed:
1. Draw a straight horizontal line across the middle of the paper. This is your principal axis.
2. Mark a point on this line to represent the lens. Usually, this point is the center of your page.
3. To the left of the lens (assuming light is coming from the left), mark a point 20 cm away. This is the object position. Draw a vertical line to represent the object. Make it 6 cm tall.
4. 14 cm to the right of the lens, draw a vertical dotted line. This represents the focal point (since we're dealing with a diverging lens, the focal point is on the same side as the object).
5. Draw a line from the top of the object parallel to the principal axis to the lens. Then, from the lens, draw a dotted line towards the focal point. The ray will appear to come from this point after passing the lens.
6. Draw another line from the top of the object straight to the center of the lens. This ray will continue undeviated.
7. The image is located where the rays appear to diverge from. Since we're dealing with a diverging lens, the image will be virtual and located on the same side as the object.
The distance to the image and the height of the image can be determined using the lens formula and magnification formula:
1. Lens formula: 1/f = 1/v - 1/u, where f is the focal length, v is the image distance, and u is the object distance. Solving for v gives us v = 1/((1/f) + (1/u)) = 1/((1/-14) + (1/-20)) cm.
2. Magnification formula: m = -v/u = h'/h, where m is the magnification, h' is the image height, and h is the object height. Solving for h' gives us h' = m*h.
Please note that the values given are in cm and that distances to the left of the lens are considered negative while distances to the right are considered positive. Similarly, a positive height indicates an upright image while a negative height indicates an inverted image.