(a) Characteristics of images formed by plane mirrors:
1. Virtual Image: The image formed by a plane mirror is always virtual, meaning it cannot be projected onto a screen. It is formed due to the reflection of light rays, but the rays do not actually converge or meet at the location of the image.

2. Laterally Inverted: The image formed by a plane mirror is laterally inverted, which means it appears flipped horizontally. For example, if you raise your right hand in front of a plane mirror, the image will show your left hand raised.

3. Same Size: The size of the image formed by a plane mirror is the same as the size of the object. There is no magnification or reduction of the image.

4. Equal Distance: The distance between the object and the mirror is equal to the distance between the image and the mirror. This property is known as the law of reflection.

(b) Using the mirror formula to determine the position and size of the image formed:

The mirror formula is given by:

1/f = 1/v - 1/u

Where:
f is the focal length of the mirror,
v is the distance of the image from the mirror (negative if it is formed on the same side as the object),
u is the distance of the object from the mirror (negative if it is formed on the same side as the object).

In this case, the object distance (u) is 20 cm, and the focal length (f) of the concave mirror is 30 cm. We need to find the image distance (v) and the size of the image.

1. Calculate the image distance (v):

1/30 = 1/v - 1/20
(20 - 30)/(30v) = 1/20
-10/(30v) = 1/20
30v = -200
v = -200/30
v = -6.67 cm

The negative sign indicates that the image is formed on the same side as the object.

2. Calculate the size of the image:

The size of the image can be determined using the magnification formula:

magnification (m) = -v/u

m = -(-6.67)/20
m = 0.333

The positive magnification indicates that the image is erect, but since the magnification is less than 1, the image is reduced in size.

Therefore, the image formed by the concave mirror is located at a distance of -6.67 cm (on the same side as the object) and it is 0.333 times smaller than the object.

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