April 29. Physics 272. Spring Prof. Philip von Doetinchem

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1 Physics 272 April 29 Spring Prof. Philip von Doetinchem Phys272 - Spring 14 - von Doetinchem - 411

2 Summary Object image relationship: Phys272 - Spring 14 - von Doetinchem - 412

3 Summary When the object is on the same side of the reflecting or refracting surface as the incoming light, the object distance s is positive; otherwise negative When the image is on the same side of the reflecting or refracting surface as the outgoing light, the radius of curvature is positive; otherwise it is negative When the center of curvature is on the same side as the outgoing light, the radius of curvature is positive; otherwise it is negative Phys272 - Spring 14 - von Doetinchem - 413

4 Refraction at a spherical surface After reflection on a spherical surface refraction on a spherical surface Essential for understanding lenses The same general laws for refraction as for a plane surfaces apply Phys272 - Spring 14 - von Doetinchem - 420

5 Refraction at a spherical surface Relationship between angles: Refraction law and other conditions: Phys272 - Spring 14 - von Doetinchem - 421

6 Refraction at a spherical surface Putting it all together: Phys272 - Spring 14 - von Doetinchem - 422

7 Refraction at a spherical surface Object-image relationship for spherical refracting surface: Very similar structure compared to the reflection case, but modified with the index of refraction Phys272 - Spring 14 - von Doetinchem - 423

8 Refraction at a spherical surface Magnification: Snell's law and small angle approximation: Phys272 - Spring 14 - von Doetinchem - 424

9 Refraction at a spherical surface Sign rule add-on: Radius is positive if the center of the curvature is on the outgoing side of the surface and negative if the center is on the other side. Phys272 - Spring 14 - von Doetinchem - 425

10 Refraction at a spherical surface Example: water droplets on plants act as spherical refraction surfaces sunlight is more concentrated plants feel a higher intensity Plane refracting surface: magnification is always 1 does not depend on index of refraction, image is erect Phys272 - Spring 14 - von Doetinchem - 426

11 Image formation by refraction Small image in front of a cylindrical glass rod: image is inverted and reduced in size Phys272 - Spring 14 - von Doetinchem - 427

12 Image formation by refraction Immerse glass rod in water (n=1.33): the refracted rays do not converge and appear to diverge from a point 21.3cm to the left from the vertex The result is a virtual image Image is still erect and the virtual image appears magnified Phys272 - Spring 14 - von Doetinchem - 428

13 Thin lenses What does thin mean? Parallel light rays cross two spherical surfaces Between surfaces material of different index of refraction (typically higher) After leaving the material: where do light rays cross the optic axis? Surfaces are close to each other with respect to the length of the lens thin lens: parallel light is focused in focal points Contacts or eye glasses are examples of thin lenses Phys272 - Spring 14 - von Doetinchem - 429

14 Thin lenses Beams of parallel light pass through the lens and converge in the focal point Each side of the lens has one focal point For a thin lens the focal length on both sides is the same (even for different radii on both sides) Phys272 - Spring 14 - von Doetinchem - 430

15 Thin lenses Construction: Parallel light ray from object is refracted in thin lens through the focal point on the other side of the lens Light going through the middle of the lens passes straight through the thin lens (no change in direction) Phys272 - Spring 14 - von Doetinchem - 431

16 Thin lenses Object-image relationship is the same as for spherical mirrors: Phys272 - Spring 14 - von Doetinchem - 432

17 Thin lenses sign rules from the discussion of spherical mirrors apply to lenses For a 3-D object the two directions perpendicular to the optic axis are reversed, the arrow along the optic axis is not reversed Phys272 - Spring 14 - von Doetinchem - 433

18 Diverging lenses Converging lens: thicker in the center than at the edges Diverging lens: thicker at the edges than at the center Parallel rays are diverged virtual image in focal point Phys272 - Spring 14 - von Doetinchem - 434

19 The Lensmaker's equation The image of the first refracting surface is used as the object position for the second refracting surface The sketch shows a distance of d between the two spherical mirrors we will set distance to zero Phys272 - Spring 14 - von Doetinchem - 435

20 The Lensmaker's equation Image position after the first surface: Image of first surface acts as object for second surface. In coming light on second surface is on the opposite side as the image from surface 1: s2=-s1' Phys272 - Spring 14 - von Doetinchem - 436

21 The Lensmaker's equation Combining both equations: For a lens in air (s1 s, s'2 s', nb = n) Phys272 - Spring 14 - von Doetinchem - 437

22 The Lensmaker's equation Focal length on both sides of the object are the same (set object distance and image distance to infinity): Be careful: rays at larger distance from optic axis are not going to the same focus point abberation Phys272 - Spring 14 - von Doetinchem - 438

23 Object position and focal point for a converging lens Object further away than focal point: Object inside focal point: light rays converge and form a real image on the other side of the lens Light rays diverge and the image is virtual and larger than the object Photography: having the sensor at the right focal point is essential for a sharp image Phys272 - Spring 14 - von Doetinchem - 439