AN OBJECT 5.0 HIGH IS PLACED 35CM FROM CONCAVE MIRROR OF FOCAL LENGTH 15CM BY DRAWING A RAY DIAGRAM.DETERMINE THE POSITION,SIZE AND NATURE OF IMAGE

I can't draw the ray diagram, here is an example

Draw yours to scale.
http://www.physicsclassroom.com/class/refln/Lesson-3/Ray-Diagrams-Concave-Mirrors

draw two rays from the tip of the five cm candle

The first one goes in hits the center of the mirror, and pops out at that same angle from the centerline
tan theta = 5/35

The second one oe twrd the mirror parallel to the center line and bounces off THROUGH the centerline 15 cm from the mirror

Where those two lines cross below the centerline is the new, upside down, candle tip of the shorter candle image

LOL - yes, just like the diagrams in the link Bob gave you !

I want answers of my questions

To determine the position, size, and nature of the image formed by the concave mirror, you can use the ray diagram method. Here's how:

Step 1: Draw the principal axis: Draw a straight horizontal line on your paper. This line represents the principal axis of the concave mirror.

Step 2: Place the object: Place the object (5.0 cm high) on the principal axis, 35 cm from the mirror. Mark this point as the object's position. Draw an arrow indicating the upward direction to represent the object.

Step 3: Locate the focal point: The focal length of the concave mirror is given as 15 cm. Measure 15 cm from the mirror along the principal axis on both sides, and mark these points as F and F'. These are the focal points.

Step 4: Draw rays: Draw three incident rays from the object to the mirror.

- Ray 1: Draw a ray parallel to the principal axis. After reflection, this ray will pass through the focal point F.
- Ray 2: Draw a ray passing through the focal point F. After reflection, this ray will be parallel to the principal axis.
- Ray 3: Draw a ray passing through the center of curvature C (located at twice the focal length from the mirror). After reflection, this ray will reflect back on itself.

Step 5: Locate the image: The image is formed by the intersection of the reflected rays.

Step 6: Measure the position of the image: Measure the distance from the mirror to the image along the principal axis. This distance is the position of the image.

Step 7: Measure the size of the image: Measure the height of the image. This will give you the size of the image.

Step 8: Determine the nature of the image: Based on the position and size of the image, determine whether it is real or virtual, magnified or diminished, and erect or inverted.

By following this ray diagram method, you will be able to determine the position, size, and nature of the image formed by the concave mirror.