2Thin LensesA thin lens consists of a piece of glass or plastic, ground so that each of its two refracting surfaces is a segment of either a sphere or a planeLenses are commonly used to form images by refraction in optical instruments (cameras, telescopes, etc.)
3Thin Lens Shapes These are examples of converging lenses They have positive focal lengthsThey are thickest in the middle
4More Thin Lens Shapes These are examples of diverging lenses They have negative focal lengthsThey are thickest at the edges
5Focal Length of LensesThe focal length, ƒ, is the image distance that corresponds to an infinite object distanceThis is the same as for mirrorsA thin lens has two focal points, corresponding to parallel rays from the left and from the rightA thin lens is one in which the thickness of the lens is negligible in comparison with the focal length
6Focal Length of a Converging Lens The parallel rays pass through the lens and converge at the focal point FThe parallel rays can come from the left or right of the lensf is positive
7Focal Length of a Diverging Lens The parallel rays diverge after passing through the diverging lensThe focal point is the point where the rays appear to have originatedf is negative
8Thin LensesWhen parallel rays pass through a converging lens, the rays converge at the focal point f of the lens. They form a real image of an object at infinity.When parallel rays pass through a diverging lens, the rays diverge away from the focal point f of the lens, and must be extrapolated back to find it. The image is virtual.
9Converging LensesA thin lens is defined here as a lens with a thickness that is small relative to its focal length. We can approximate the lens behavior by assuming that the incident rays are bent as they pass through the plane of the lens.Parallel incident rays are brought to a focus beyond the lens at the downstream focal point f.Incident rays that pass through the upstream focal point f become parallel beyond the lens.Incident rays that pass through the center of the lens are not deflected.
10Real ImagesThe rays diverge from point P on the object, are refracted by the lens, and converge to form a real inverted image at point P’ on the image.All points that lie in the same plane on the object (P, Q, R) will converge at corresponding points (P’, Q’, R’) on the image plane.The close-up view shows rays very near the image plane.
11Ray Diagrams for Thin Lenses Ray diagrams are essential for understanding the overall image formation.Three rays are drawn:The first ray is drawn parallel to the first principle axis and then passes through (or appears to come from) one of the focal points.The second ray is drawn through the center of the lens and continues in a straight line.The third ray is drawn from the other focal point and emerges from the lens parallel to the principle axisThere are an infinite number of rays, these are the convenient ones.
12Converging Lens Ray Tracing 1. Draw the lens.2. Draw the optical axis through the center of the lens, with the focal points f placed symmetrically on both sides.3. Represent the object with an upright arrow of height h at distance s.4. Draw the three “special” rays from the tip of the object arrow:(a) A ray from the arrow tip parallel to the axis => right focus;(b) A ray from the arrow tip through the left focus => parallel;(c) A ray from the arrow tip through the lens center => straight.5. Extend the rays until they converge (at the image arrow tip).
13Magnification1. A positive value of M indicates that the image is upright relative to the object. A negative value of M indicates that the image is inverted relative to the object.2. The absolute value of M gives the size ratio of image to object:h’/h = |M|.Note that even though M is called “magnification”, its magnitude can be less than 1, indicating that the image is smaller than the object, (i.e., it is demagnified).
14Virtual ImagesThe rays diverge from point P on the object (which is inside f ), are refracted by the lens, and still diverge after the lens. However, if the downstream rays are extrapolated backwards, these extrapolated rays converge to a virtual image at P’.In the case shown, the virtual image is upright and has a magnification greater than 1. The rays reaching the eye appear to be coming from the virtual image.
15Diverging LensesA lens that is thicker at the edges than at the center is called a diverging lens.Parallel incident rays, after passing through the lens, will diverge from a virtual focus point behind the lens, at the upstream focal point f.Incident rays converging toward the downstream focal point f become parallel after passing through the lens.Incident rays that pass through the center of the lens are not deflected.
16Diverging Lens Ray Tracing 1. Draw the lens.2. Draw the optical axis through the center of the lens, with the focal points f placed symmetrically on both sides.3. Represent the object with an upright arrow of height h at distance s.4. Draw the three “special” rays from the tip of the object arrow:(a) A ray from the arrow tip parallel to the axis => from left focus;(b) A ray from the arrow tip toward the right focus => parallel;(c) A ray from the arrow tip through the lens center => straight.5. Extrapolate these rays backwards until they converge.
17Ray Diagram for Converging Lens, p > f The image is realThe image is inverted
18Ray Diagram for Converging Lens, p < f The image is virtualThe image is upright
19Ray Diagram for Diverging Lens The image is virtualThe image is upright
21Lens Equation, cont.The equation can be used for both converging and diverging lensesA converging lens has a positive focal lengthA diverging lens has a negative focal length
22Sign Conventions for Thin Lens QuantityPositive WhenNegative WhenObject location (p)Object is in front ofthe lensObject is in back ofImage location (q)Image is in back ofImage is in front of thelensImage height (h’)Image is uprightImage is invertedR1 and R2Center of curvature isin back of the lensin front of the lensFocal length (f )Converging lensDiverging lens
23The Thin Lens Equation Sign Conventions: do is positive for real objects (from which light diverges)do is negative for virtual objects (toward which light converges)di is positive for real images (on the opposite side of the lens from the object)di is negative for virtual images (same side as object)f is positive for converging (convex) lensesf is negative for diverging (concave) lensesm is positive for upright imagesm is negative for inverted images
24Example 1An object is placed 20 cm in front of a converging lens of focal length 10 cm. Where is the image? Is it upright or inverted? Real or virtual? What is the magnification of the image?do = 20 cmf = 10 cmReal image
25Example 2An object is placed 5 cm in front of a converging lens of focal length 10 cm. Where is the image? Is it upright or inverted? Real or virtual? What is the magnification of the image?do = 5 cmf = 10 cmVirtual image
26Example 3An object is placed 8 cm in front of a diverging lens of focal length 2.67 cm. Where is the image? Is it upright or inverted? Real or virtual? What is the magnification of the image?do = 8 cmf = cmVirtual
27Combinations of Thin Lenses The key point to remember is that the image produced by one lens serves as the object for the next lens.The total magnification of a compound lens system is the product of the individual magnification factors:mtotal=m1 m2 m3….
28Example 4(a)Determine the distance from lens 1 to the final image for the system shown in the figure.(b) What is the magnification of this image?When you have twolenses, the imageof the first lens isthe object for thesecond lens.