Lecture #12 Review Total Internal Reflection and Convex Lenses

1. Lecture #12Review Total Internal ReflectionandConvex Lenses March, 1st

2. Agenda • Review Total Internal Reflection. • 3. Convex Lenses • 4. Quiz #2 • The workshops planned for this week: • #11 Refraction • #12 Convex Lenses

3. Summary on TIRLight goes from a dense medium to a less-dense medium.Then, the refraction angle 2 exceeds the incidence angle 1.This statement is Snel’s Law in qualitative form.Now:Increase 1 :Since θ2 > θ1,2 will reach 90 degrees.if θ1 is sufficiently large.

4. Total Internal Reflection An effect that combines both refraction and reflection is total internal reflection. Consider light coming from a dense medium like water into a less dense medium like air.

5. Total Internal Reflection n=1 n=1.333 Critical angle How large is large?

6. The value of 1(when 2 = 90 degrees) is called the critical anglec.Then, the refracted beam skims the surface. Suppose we increase the incident angle θ1 to values beyond the critical angle θc. Then, no light is transmitted. We have total internal reflection (TIR).Conditions for TIR:1. The light is in a more dense medium and approaches a less dense medium;2. The angle of incidence is greater than the critical angle.n=1.333--->n=1 (?); n=1.333--->n=1.52 (?)

7. What is the Critical Angle? Value of c Let: n = refractive index of original medium, Let air or vacuum be the other medium. n = 1.0 for air or vacuum.  Apply Snell’s Law: n1 sin 1 = n2 sin 2 . Can now replace n2 by 1: n1 sin 1 = sin 2 .

8. We now make the incident angle equal to the critical angle:Insert: 1 = c . Then, 2 = 90 degreesnsin  = sin (90 degrees) = 1.Here, we have set n to be the refractive index of the original medium.Solve for the critical angle: sin c = 1/n.This equation gives us the critical angle.

9. For optical fibers, want c to be small. • So, choose n large. • Optical fibers: the fibers pipe light from one place to another • The light rays bounce along the inner walls

10. Taking Advantage of Refraction The greater the density difference between the two materials, the more the light bends. One place where this is used is in lenses for a variety of optical devices, such as microscopes, magnifying glasses, and glasses for correcting vision. An example of an image formed from a lens is shown below.

11. Refraction and Thin Lenses Can use refraction to try to control rays of light to go where we want them to go. Let’s see if we can FOCUS light.

12. Refraction and Thin Lenses What kind of shape do we need to focus light from a point source to a point? lens with some shape for front & back point source of light screen di = image distance d0 = object distance

13. Lenses A lens is a material body with two refracting surfaces. Light enters the front surface, and exits the back surface. Assume that both surfaces are spherical. The line through their centers is the principal axis (PA) of the lens. The lens is constructed so that the PA is normal to both spherical surfaces.

14. How Does a Lens Bend Light? Suppose we have light from a very distant source S. Then, all the light rays are parallel to each other. Let S be located so that the line from S to the lens-center is the the PA. Take the case in which the lens is convex. This means that the lens is thicker at its center, than at its edges.

15. What happens to the light? Consider only thin lenses. That is, the lens thickness is small, relative to the radii of curvature. Assume that the refractive index of the lens exceeds that of its surroundings, (usually air). From experiment, we find: All the rays meet at one point on the PA. This point is called the focal point F. It is on the opposite side of the lens. Restate this result: The point F is the image point for an object at infinity, on the lens axis. The distance of F to the lens-center is called the focal length f. The power P of the lens is defined by P = 1/f. Its unit is the diopter, or inverse meter.

16. The Lensmaker’s Equation What does Snel’s Law say about light entering the lens? How is it bent? It predicts the same result as is found empirically. The light rays parallel to the PA meet at one point F, at a distance f from the lens-center. But: Theory also gives us a result for f. This is the lensmaker’s equation: 1/f = (n -1){(1/R(1)+1/R(2)}. Here, R(1) and R(2) are the radii of the two surfaces of the lens.

17. Source not on the Principal Axis. Suppose that the source S is distant, but not on the PA. The, both theory and experiment show that; All the rays again meet at one point. This point is on the focal plane. By definition, the focal plane is perpendicular to the PA, and through F.

18. Sources that are not distant Where is the image located, for any object? Let d0 be the distance of an object point to the lens Let di be the distance of the image point to the lens. Both of these two distances are measured along the PA direction. The lens equation gives di, if d0 and f are known. The equation is 1/f = (1/d0) + (1/di). Question for you: What would you expect the value of d to be, if the object is at infinity? Does the lens equation agree with this?

19. Supplementary - textbook: Chapter 23, TIR, Fiber optics, pp. 645-646, Lenses, pp. 647-651

20. Quiz #2 Questions: 1. What is the law of reflection? 2. What is the ray approximation (RA)? 3. Explain a rainbow. 4. Explain dispersion through a prism. 5. What is Snell’s law? Bonus: 6. What are the conditions for Total Internal Reflection?