LENS any transparent object having two nonparallel curved surfaces or one plane surface and one curved surface Converging Lenses - thicker in middle than in the edge These lenses converge light to a real focus.

double concaveplano-concave These lenses diverge light from a virtual focus. Diverging Lenses - thicker at edge than in middle

Ray Diagrams Converging and Diverging Lenses Incident rays parallel to the principal axis refract through the focus or diverge away from the focus. 1. Rays passing through or toward the focus refract parallel to the principal axis. Just like mirrors, 1/f = 1/d o + 1/d i and d i /d o = h i /h o.

Click here, here, and here to view here simulations showing image formation in converging and diverging lenses using these three important rays.

Images formed by converging lenses may be: 1. real, virtual, or non-existent 2. upright or inverted 3. reduced, enlarged, or same size 4. in front or behind the lens The simulation linked here here shows image formation in a converging lens. Learn more about image characteristics here. here

The image characteristics depend on the object’s position with respect to one and two focal lengths (1f and 2f) away from the lens. 2ff

object is exactly twice the focal length: image is real, inverted, and the same size object between one and two focal lengths: image is real, inverted, and enlarged object is on the focus: no image; rays reflect parallel object is inside the focus: image is virtual, upright, and enlarged object is beyond two focal lengths: image is real, inverted, and reduced

Images formed by diverging lenses are always: 1. virtual 2. upright 3. reduced 4. located in front of the lens between the focus and the lens focus and the lens The simulation linked here here shows image formation in a diverging lens. Learn more about image characteristics here. here

General Image Trends real images are always inverted real images are always inverted virtual images are always upright virtual images are always upright real images are always behind the lens real images are always behind the lens virtual images are always in front virtual images are always in front of the lens negative image distance means negative image distance means virtual image positive image distance means real image positive image distance means real image real images may be projected onto a screen; virtual images may not real images may be projected onto a screen; virtual images may not