Spherical mirror Formula

This equation predicts the formation and position of both real and virtual images in thin spherical lenses. It is valid only for paraxial rays, rays close to the optic axis, and does not apply to thick lenses. Also, it can be determined the curvature ratio of the lens.

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

Focal length ≈ curvature radius / 2

The equations are:

1/o + 1/I = 1/f

F ≈ r/2

Where:

o: Object distance

I: Formed image distance

f: focal length

r: Curvature radius

Spherical mirror 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/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 and its curvature radius?

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

then it curvature radius is

r ≈ 2 * f = 40 cm