Lecture 23 Chapter 34 Physics II Ray Optics Thin Lenses Course website: http://faculty.uml.edu/andriy_danylov/teaching/physicsii
Today we are going to discuss: Chapter 34: Section 34.5-6 Thin Lenses
There are two types of lenses A converging lens causes the rays to refract toward the optical axis. A diverging lens refracts parallel rays away from the optical axis A converging lens is thicker in the center than at the edges. A diverging lens is thicker at the edges than in the center.
Lensmaker s Equation This useful equation relates the radii of curvature of the two lens surfaces, and the index of refraction, to the focal length: 1 1 1 1
Converging Lens
There are three typical situations which are used in Ray Tracing for a converging lens: A ray initially parallel to the optic axis will go through the far focal point after passing through the lens. A ray through the near focal point of a thin lens becomes parallel to the optic axis after passing through the lens. A ray through the center of a thin lens is neither bent nor displaced but travels in a straight line. Case 1 Case 2 Case 3 (Focusing the Sun) (Reversing the case 1) (Trivial)
1) Ray Tracing Consider a converging lens for which the object is outside the focal point, at distance s >f. Object 1 h 2 3 O F 2 Optical axis F 1 h' Near focal point S Object distance S f f (focal length) Far focal point Image distance Image (inverted real image) How to test if an Image is real? 1) Either, an image can be seen on a screen 2) Or, An image is created by converging rays Examples of real Demo: cat/flashlight/screen/lens inverted images To demonstrate how to test a real image
Thin-lens equation For a converging lens f is positive f > 0 If after using the lens equation, s > 0 If after using the lens equation, s < 0 2) Algebraic Method In order to use this formula properly we have to obey the sign convention S > 0 is positive all the time s>0 For a diverging lens f is negative f < 0 Magnification Image is real Image is virtual The sign conventions (summary) Focal length,f Image distance, s Magnification, m Object distance, s f > 0 converging lens s > 0, real image m> 0, upright image s > 0 always The image can be either larger or smaller than the object, depending on the location and focal length of the lens. Δ The magnification m is defined as: Δ f < 0 diverging lens s < 0, virtual image m< 0, inverted image s > 0 always The minus is introduced so that: m>0 indicates that the image is upright relative to the object. m<0 indicates that the image is inverted relative to the object.
Converging lens. Virtual Image Consider a converging lens for which the object is inside the focal point, at distance s < f. Image (virtual image in upright position) h' 2 1 3 F h 2 F Object 1 S S f How to test if an Image is real/virtual? Since the image is created by diverging rays and cannot be seen on a screen, the image is virtual
You can see a virtual image by looking through the lens. This is exactly what you do with a magnifying glass, microscope or binoculars. Virtual Magnified Images Doc uses a magnifying glass in 1955 to read the letter written by his 1985 counterpart.
Diverging Lens
There are three typical situations which are used in Ray Tracing for a diverging lens: Case 1 (Still thinking about a name) Case 2 (Reversing the case 1) Case 3 (Trivial)
a) Ray Tracing Consider a diverging lens for which the object is outside the focal point, at distance s > f. You can see all three rays appear to diverge from point P. Point P is an upright, virtual image of the object point P. h (virtual image in upright position) S h' F 1 O F 2 f S Optical axis b) Algebraic method Let s find an image distance s using the lens equation Note!!! For a diverging lens f is negative f < 0 and S > 0 is positive all the time Solve for s 100 50 s is negative, so 33.3 100 50 Image is virtual Let s find magnification using (And we got the same answer graphically) A positive value of m indicates that the.. image is upright relative to the object.
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