Refraction & Lenses

1. Refraction & Lenses Chapter 15

2. Refraction • The bending of light as it changes from one medium to another. • Results from a change in speed of the light. • Some portions of the light beam slow down before others, resulting in a bend. • Refraction doesn’t occur if light is coming in perpendicular to the surface.

3. Index of Refraction • Index of Refraction is a measure of both how much light bends in a medium and how fast the light is moving in the medium. • By definition: • Since index of refraction is usually given, instead we usually use the form:

5. Refraction Terminology • Like reflection, all angles are measured from the normal. • One medium is labeled 1 and the other 2. Doesn’t matter which is which as long as you are consistent.

6. Snell’s Law • A ray of light goes from water into quartz. If the angle of incidence is 21 degrees, what is: • The angle of refraction? • The change in speed of the light? • A light ray with an angle of incidence of 55 degrees goes from water to the air. What is the angle of refraction?

7. Total Internal Reflection • When light moves from a medium with a higher n to one with a lower n, there are certain angles for which Snell’s Law cannot be satisfied. • Instead, the light reflects back into the first medium. • The transition angle (ray 4) is called the critical angle. The light just skims the surface. • Anything greater than the critical angle (ray 5) will totally internally reflect.

8. Critical Angle • Symbol is θc • For water to air, the critical angle is 48.6 degrees. • If n1 is the medium with the higher n, then: • When light moves from medium A to medium B at an angle of incidence of 23 degrees, its angle of refraction is 41 degrees. What is the critical angle from A to B?

9. Fiber Optics • Cables that use TIR to bounce a signal back and forth. • Light ray will always hit the opposite side at greater than the critical angle and therefore completely bounce back. • Transmission without loss.

10. Random Practice • Scuba Barbie goes swimming in the pool. When she dives to a depth of 4m, a light ray that leaves her and exits the pool 1m away from the edge refracts at an angle of 78 degrees. How far from the edge of the pool is she? • In the picture, the slab of diamond is 3cm thick. The angle of incidence is 31 degrees. If the refracted ray is 0.35cm away from the blue ray as it exits the diamond, what is the index of refraction of the top medium?

11. Effects of Refraction • Mirages – Hot air is less dense above the road and has a lower index of refraction. Light refracts as is moves through this hot air and you see the image of inverted objects in the distance. The look like reflections but are actually due to refraction. • Longer Days – Differing air density in the upper atmosphere causes sunlight to refract when rising or setting. This allows us to see sun before it actually rises or sets. It causes days to be longer. • Where is the fish? - Your eyes (and brain) are used to light traveling in a straight line. When you reach for something in water, you will reach above where the object is actually located due to refraction.

12. Prisms • Different wavelengths of light have different n’s. Therefore, when light comes into mediums where this effect is pronounced, the colors will split. • Splitting of colors due to different n’s is called dispersion

13. Lenses • Convex lenses are those which bubble out • Similar to concave mirrors • Sometimes called converging lenses. • Concave lenses are those that cave in • Similar to convex mirrors • Sometimes called diverging lenses • Lenses that are curved on both sides have two C’s and two F’s

14. Lens Rules • Incident rays which are parallel to the principle axis will refract through the focus. • Incident rays that go through the focus will refract parallel to the principle axis • Incident rays that pass through the middle of the lens are not bent.

15. Convex Lens • Incident rays which are parallel to the principle axis will refract through the focus. • Incident rays that go through the focus will refract parallel to the principle axis. • Incident rays that pass through the middle of the lens are not bent.

16. Object on C • Incident rays which are parallel to the principle axis will refract through the focus. • Incident rays that go through the focus will refract parallel to the principle axis. • Incident rays that pass through the middle of the lens are not bent.

17. Object between C and F • Incident rays which are parallel to the principle axis will refract through the focus. • Incident rays that go through the focus will refract parallel to the principle axis. • Incident rays that pass through the middle of the lens are not bent.

18. Object on F • Incident rays which are parallel to the principle axis will refract through the focus. • Incident rays that go through the focus will refract parallel to the principle axis. • Incident rays that pass through the middle of the lens are not bent.

19. Object between F and Lens • Incident rays which are parallel to the principle axis will refract through the focus. • Incident rays that go through the focus will refract parallel to the principle axis. • Incident rays that pass through the middle of the lens are not bent.

20. Concave Lens • Incident rays which are parallel to the principle axis will refract through the focus. • Incident rays that go through the focus will refract parallel to the principle axis. • Incident rays that pass through the middle of the lens are not bent.

21. The Lens Equation

22. Practice Problems • A banana is placed along the principle axis of a thin converging lens that has a focal length of 22cm. If the distance from the object to the lens is 36cm, what is the distance from the image to the lens? • An image distance is 4.5 times the focal length of a lens. • What is the object distance in terms of f? • If the object is 3.5cm wide, how wide is the image?

23. Practice Problems • An object is placed 20.0 cm in front of a converging lens of focal length 10.0 cm. Find the image distance and the magnification. Describe the image. • An object is placed 20 cm in front of a diverging lens of focal length 10.0 cm. Find the image distance and magnification. • Fill in the missing values in the following table:

24. Normal Vision • The distance between the lens of your eye and where the retina is constant. • Therefore, your eyes use muscles around your lens to change its focal length so the image always appears on the retina.

25. Vision Problems • Myopia-nearsightedness • The eyeball is elongated causing objects far away to focus in front of the retina • Corrected with concave lenses which spread the light out prior to its entrance to the eye.

26. Farsightedness • Hyperopia • Opposite of myopia. • Eyeball is shortened causing light to focus behind the retina for near distances • Presbyopia • Age related farsightedness • Eyeball loses its elasticity and can no longer focus properly for near objects.