To determine the image distance and image height for an object placed 20 cm in front of a converging lens with a focal length of 15 cm, we can use the lens equation and magnification formula.

The lens equation is:

1/f = 1/di + 1/do

Where f is the focal length, di is the image distance, and do is the object distance.

Since the object distance (do) is given as 20 cm and the focal length (f) is given as 15 cm, we can substitute these values into the lens equation:

1/15 = 1/di + 1/20

To solve for di, we can multiply both sides of the equation by 300 (the least common multiple of 15 and 20) to eliminate the fractions:

300/15 = 300/di + 300/20
20 = 300/di + 15

Rearranging the equation gives us:

5 = 300/di

Cross-multiplying gives us:

5di = 300

Simplifying for di gives us:

di = 300/5
di = 60 cm

Therefore, the image distance for the object placed 20 cm in front of the lens is 60 cm.

To calculate the image height (hi), we can use the magnification formula:

m = -di/do = hi/ho

Where m is the magnification, di is the image distance, do is the object distance, hi is the image height, and ho is the object height.

If the object height (ho) is not given, we assume it to be 1 (unit height). Therefore, the magnification (m) is equal to the image height (hi).

Using the given magnification formula, we have:

m = -di/do
m = -60/20
m = -3

Therefore, the image height for the object is -3 (as it is inverted).

In summary, the image distance for the object placed 20 cm in front of a converging lens with a focal length of 15 cm is 60 cm, and the image height is -3.

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