The magnification (m) of an image formed by a mirror is given by the ratio of the image height (h') to the object height (h), which is also equal to the ratio of the image distance (d') to the object distance (d). The formula is:

m = -d'/d = h'/h

In a diverging mirror, the image distance is negative. The formula for the image distance in a mirror is given by the mirror equation:

1/f = 1/d + 1/d'

where f is the focal length, d is the object distance, and d' is the image distance. We can rearrange this equation to solve for d':

d' = 1/(1/f - 1/d)

Substituting the given values:

d' = 1/(1/(-15 cm) - 1/(10 cm)) = -6 cm

The negative sign indicates that the image is virtual and located on the same side of the mirror as the object.

Now we can calculate the magnification:

m = -d'/d = -(-6 cm)/(10 cm) = 0.6

So, the magnification of the image is 0.6. This means the image is 0.6 times the size of the object, or 60% of the original size.

Question

The magnification (m) of an image formed by a mirror is given by the ratio of the image height (h') to the object height (h), which is also equal to the ratio of the image distance (d') to the object distance (d). The formula is:

m = -d'/d = h'/h

In a diverging mirror, the image distance is negative. The formula for the image distance in a mirror is given by the mirror equation:

1/f = 1/d + 1/d'

where f is the focal length, d is the object distance, and d' is the image distance. We can rearrange this equation to solve for d':

d' = 1/(1/f - 1/d)

Substituting the given values:

d' = 1/(1/(-15 cm) - 1/(10 cm)) = -6 cm

The negative sign indicates that the image is virtual and located on the same side of the mirror as the object.

Now we can calculate the magnification:

m = -d'/d = -(-6 cm)/(10 cm) = 0.6

So, the magnification of the image is 0.6. This means the image is 0.6 times the size of the object, or 60% of the original size.

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