Image position Formula

This equation predicts the formation and position of both real and virtual images in thin lenses. It is valid only for paraxial rays, rays close to the optic axis, and does not apply to thick lenses.

1/(object distance) + 1/(image distance) = 1/(focal length)

The equation is:

1/o + 1/I = 1/f

Where:

o: Object distance

I: Formed image distance

f: focal length

Image position Formula Questions:

1) A lens with focal distance of 30 cm is placed in front of an object, which is located at 1 m from it. Where is image of the object located?

Answer:

From the image position formula:

1/o + 1/I = 1/f

1/(100 cm) + 1/I = 1/(30 cm)

1/(30 cm) – 1/(100 cm) = 1/I

1/I =0.023/cm

I = 42.85 cm

2) A lens forms an image at 25 cm from it, where the real object is placed at 1 m, what is the focus length of the lens?

Answer:

From the image position formula, we find:

1/f = 1/o + 1/I = (o+I)/(o*I)

f = o*I/(o+I) = 25 cm * 100 cm² /(125 cm)

f = 2500/125 cm = 20 cm