8. Thin lenses 1) Types of lenses Thin lenses are those whose thickness is small compared to their radius of curvature. They may be either converging or diverging. 1) Types of lenses Example: An air bubble in a piece of glass has a double convex shape (see below). What type of the lens is formed? Converging Diverging It depends on if nin > nout if nin > nout

2) Focus and focal plane A diverging lens make parallel light diverge. The focal point is that point where the diverging rays would converge if projected back. Parallel rays are brought to a focus by a converging lens.

+ f > 0 f > 0 3) Main equations Thin lens equation Lensmaker’s equation Magnification Note! We use different sign convention than in the Giancoli book Lens power: is measured in diopters, D. For mirrors and lenses we assume that the radius R is positive if the center is on the side of the outgoing (passing) rays, and that R is negative otherwise. R1>0 C2 C1 + R2<0 f > 0 f > 0

4a) Ray tracing (thin converging lenses) f > 0

f < 0 4b) Ray tracing (thin diverging lenses) 4 2F 2F The image is upright and virtual Ray 1 leaves the top of the object and is drawn such that it is parallel to the axis; it emerges from the lens along a line through the focal point on the back side of the lens Ray 2 leaves the top of the object and is made to pass through the other focal point; it emerges from the lens parallel to the axis. Ray 3 leaves the top of the object and is directed toward the very center of the lens; it emerges from the lens a the same angle as it entered. Ray 4 leaves the top of the object and is directed toward 2F on the opposite side of the lens; it emerges from 2F on the same side as the object.

Converging lenses Diverging lenses

magnification image mirror/lens do di m<0 inverted, real concave/converging do>f di>f m>1 0<m<1 upright, virtual convex/diverging 0<do<f 0<do di<0 -f<di<0

Example 1: The images formed by concave lenses are always real are always virtual C) could be real or virtual; it depends on whether the object distance is smaller or greater than the focal length D) could be real or virtual, but always real when the object is placed at the focal point Example 2: An object is placed between a convex lens and its focal point. The image formed is A) virtual and erect B) virtual and inverted C) real and erect D) real and inverted Example 3: A convex lens has a focal length f. An object is placed between f and 2f on the axis. The image formed is located A) at 2f B) between f and 2f C) at f D) at a distance greater than 2f from the lens

Example 1: A thin symmetric lens provides an image of a fingerprint with a magnification +0.2 when the fingerprint is 1 cm farther from the lens than the focal point of the lens. What is the type of the image, and what is the type of the lens? Answer: Image is erect and virtual; this is diverging lenses Example 2: A glass converging lens has one flat side and another with a radius of 20 cm. What is the focal length of the lens? ( The index of refraction of the glass in the lens is 1.50)