Verified answer

Answer:

Magnification = 2 and Nature = Virtual and Erect.

Explanation:

To determine the magnification and nature of the image formed by a concave mirror, we can use the mirror formula:

Mirror Formula: 1/f = 1/v + 1/u

Where:

f = focal length of the concave mirror

v = image distance from the mirror (negative for virtual image)

u = object distance from the mirror (negative for real object)

Given data:

Height of the object (h) = 3 cm

Distance of the object from the mirror (u) = -15 cm (since it is in front of the mirror, the distance is negative)

Distance of the image from the mirror (v) = -30 cm (since it is 30 cm away on the front side, the distance is negative)

Now, let's calculate the focal length (f) of the concave mirror using the mirror formula:

1/f = 1/v + 1/u

1/f = 1/(-30) + 1/(-15)

1/f = -1/30 - 2/30

1/f = -3/30

f = -30/3

f = -10 cm

The focal length (f) of the concave mirror is -10 cm.

Now, let's calculate the magnification (M) of the image:

Magnification (M) = Height of the image (h') / Height of the object (h)

M = h' / h

Since the image distance (v) is negative, the image is virtual and erect. Therefore, the height of the image (h') is positive.

Now, using the magnification formula:

M = -v / u

M = -(-30) / (-15)

M = 2

The magnification (M) is 2.

Now, we have the magnification and nature of the image:

Magnification = 2 (It is magnified by a factor of 2)

Nature of the image = Virtual and Erect

So, the correct pair is: Magnification = 2 and Nature = Virtual and Erect.