Physics 1202: Lecture 23 Today’s Agenda Announcements: –Lectures posted on: –HW assignments, etc. Homework #7:Homework #7: –Due next Friday

o i f h’h’ h R   h h’h’ o-R R-i o i &

Mirror – Lens Definitions Some important terminology we introduced last class, –o = distance from object to mirror (or lens) – i = distance from mirror to image o positive, i positive if on same side of mirror as o. –R = radius of curvature of spherical mirror –f = focal length, = R/2 for spherical mirrors. –Concave, Convex, and Spherical mirrors. –M = magnification, (size of image) / (size of object) negative means inverted image R     object  h image o i

Summary We have derived, in the paraxial (and thin lens) approximation, the same equations for mirrors and lenses: when the following sign conventions are used: Variable f > 0 f < 0 o > 0 o < 0 i > 0 i < 0 Mirror concave convex real (front) virtual (back) real (front) virtual (back) Lens converging diverging real (front) virtual (back) real (back) virtual (front)

This could be used as a projector. Small slide on big screen This is a magnifying glass This could be used in a camera. Big object on small film Upright Enlarged Virtual Inverted Enlarged Real Inverted Reduced Real 3 Cases for Converging Lenses ImageObject Inside F Object Image Past 2F Image Object Between F & 2F

1) Rays parallel to principal axis pass through focal point. 2) Rays through center of lens are not refracted. 3) Rays toward F emerge parallel to principal axis. F F Object P.A. Image is virtual, upright and reduced. Image Diverging Lens Principal Rays

Lecture 23, ACT 1 A lens is used to image an object on a screen. The right half of the lens is covered. –What is the nature of the image on the screen? (a) left half of image disappears (b) right half of image disappears (c) entire image reduced in intensity object lens screen

Multiple Lenses We determine the effect of a system of lenses by considering the image of one lens to be the object for the next lens. For the first lens: o 1 = +1.5, f 1 = +1 For the second lens: o 2 = +1, f 2 = -4   f = +1 f =

Multiple Lenses Objects of the second lens can be virtual. Let’s move the second lens closer to the first lens (in fact, to its focus): For the first lens: o 1 = +1.5, f 1 = +1 For the second lens: o 2 = -2, f 2 = -4   Note the negative object distance for the 2nd lens. f = +1 f =

Multiple Lenses If the two lenses are thin, they can be touching – i.e. in the same position. We can treat as one lens. f total = ?? ? Adding, For the first lens: o=o 1, i 1 and f 1 For the second lens: o 2 = -i 1, i 2 =i, f 2 As long as,

The Lens Equation –Convergent Lens: i f h’h’ o h

The Lensmaker’s Formula So far, we have treated lenses in terms of their focal lengths. How do you make a lens with focal length f ? Start with Snell’s Law. Consider a plano-convex lens: Snell’s Law at the curved surface: The bend-angle  is just given by: The bend-angle  also defines the focal length f: The angle  can be written in terms of R, the radius of curvature of the lens : Putting these last equations together, R N air h     light ray Assuming small angles,

More generally…Lensmaker’s Formula Two curved surfaces… Two arbitrary indices of refraction R > 0 if convex when light hits it R < 0 if concave when light hits it The complete generalized case… Note: for one surface Planar,

Compound Microscope o1o1 h O I2I2 h2h2 f eye h1h1 I1I1 i1i1 Objective (f ob < 1cm) f ob L Eyepiece (f eye ~5cm) Magnification:

Refracting Telescope Star f eye I2I2 h2h2 f ob Objective (f ob ~ 250cm) Eyepiece (f eye ~5cm) i1i1 I1I1 h1h1 Angular Magnification:    

~f e I1I1 eyepiece I2I2 ~f o objective L The EYE

Retina To brain The Eye What does the eye consist of? –Sphere (balloon) of water. - An aperture that controls how much light gets through – the Iris/pupil - Bulge at the front – the cornea - A variable focus lens behind the retina – the lens - A screen that is hooked up to your brain – the retina Cornea Iris Lens