To calculate the image position and magnification for an object placed 20 cm from a concave mirror with a radius of curvature of 30 cm, we can use the mirror formula and magnification formula.

1. Image Position (distance): The mirror formula is given by: 1/f = 1/v – 1/u

where: f = focal length of the concave mirror v = image distance (distance of the image from the mirror) u = object distance (distance of the object from the mirror)
Since the concave mirror has a radius of curvature of 30 cm, the focal length (f) is half the radius, so f = 15 cm.
Plugging in the values: 1/15 = 1/v – 1/20
Rearranging the equation and solving for v: 1/v = 1/15 + 1/20 1/v = (4 + 3)/60 1/v = 7/60 v = 60/7 cm
Therefore, the image is formed at a distance of approximately 8.57 cm from the mirror.

1. Magnification: The magnification (m) is given by the formula: m = -v/u

Plugging in the values: m = -(60/7) / 20 m = -3/7
The negative sign indicates that the image formed is inverted.
Therefore, the image is formed approximately 8.57 cm from the mirror, and the magnification is approximately -3/7.