An object is placed at 40 cm from a concave mirror of focal length 30 cm. The image is

Solution:

Given:

Object distance, u = -40 cm (according to the sign convention for mirrors, object is placed to the left)

Focal length of concave mirror, f = -30 cm (focal length of a concave mirror is negative)

Using the mirror formula:

1/f = 1/v + 1/u

Rearranging to solve for image distance (v):

1/v = 1/f - 1/u

1/v = 1/(-30) - 1/(-40)

1/v = -1/30 + 1/40

To combine the fractions, find a common denominator, which is 120:

1/v = (-4/120) + (3/120)

1/v = (-4 + 3) / 120

1/v = -1/120

v = -120 cm

The negative sign for 'v' indicates that the image is formed on the same side as the object (in front of the mirror), which means it is a real image. Real images formed by mirrors are always inverted.

Now, let's calculate the magnification (m) to determine the size and orientation of the image:

m = -v/u

m = -(-120 cm) / (-40 cm)

m = 120 / (-40)

m = -3

The negative sign for 'm' confirms that the image is inverted.

The magnitude of magnification |m| = 3, which is greater than 1. This indicates that the image is enlarged.

Therefore, the image formed is Real, Inverted, and Enlarged.