Information for Physics 1201 Midterm 2 Wednesday, March 27

Transcription

1 My lecture slides are posted at Information for Physics 1201 Midterm 2 Wednesday, March 27 1) Format: 10 multiple choice questions (each worth 5 points) and two show-work problems (each worth 25 points), giving 100 points total. 2) Closed book and closed notes. 3) Equations and constants will be provided on the midterm 4) Covers the material in Chapters 21, 22, 23, and 24

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3 Polarization Polarized light is produced by the scattering of unpolarized sunlight by molecules in the atmosphere. Molecules re-radiate sunlight. As you look at larger and larger angles with respect to the incident sunlight, the re-radiated light becomes more and more horizontally polarized.

4 Polaroid Sun Glasses Besides sunlight re-radiated from atmospheric molecules, there are other sources of horizontally polarized light that occur in nature, such as sunlight reflected from horizontal surfaces such as lakes. Polaroid sun glasses take advantage of this fact by using polarizers with their axes oriented vertically: è in addition to 1/2 of the unpolarized light which is already blocked by the polarizers, all of the horizontally polarized light is completely blocked, thus blocking out some of the reflected light which can confuse you during some outdoor activities (e.g. driving, piloting, fishing.).

5 Polarization Another application using polarized glasses: watching 3-D movies. In a 3-D movie, two separate rolls of film are projected using a projector with two lenses, each with its own polarizer. The two polarizers are crossed. Viewers watch the action on-screen through glasses that have correspondingly crossed polarizers for each eye. IMAX movie projector Movie viewer using polarized glasses

6 Example. Partially polarized and partially unpolarized light. A light beam passes through a polarizer whose transmission axis makes angle θ with the vertical. The beam is partially polarized and partially unpolarized, and the average intensity of the incident light, S 0, is the sum of the average intensity of the polarized light, S 0,polar, and the average intensity of the unpolarized light, S 0,unpolar. As the polarizer is rotated clockwise, the intensity of the transmitted light has a minimum value of 2.0 W/m 2 when θ = 20.0 o and has a maximum value of 8.0 W/m 2 when the angle is θ = θ max. è Find a) S 0,unpolar, and b) S 0,polar. Incident light S 0 = S 0,polar + S 0,unpolar Transmitted light S = S polar + S unpolar

7 Incident light S 0 = S 0,polar + S 0,unpolar Transmitted light S = S polar + S unpolar a) Minimum transmitted intensity S = S min = 2.0 W/m 2 at θ = 20.0 o. S is minimum when S polar = 0 since S unpolar is not effected by θ. S unpolar = S min - S polar = = 2.0 W/m 2 S unpolar = ½ S 0,unpolar è S 0,unpolar = 2S unpolar = 2(2.0) = 4.0 W/m 2 b) Maximum transmitted intensity S = S max = 8.0 W/m 2 occurs at θ max. S is maximum when S polar = S 0,polar (when θ = 20 o + 90 o = 110 o = θ max ) S max = S 0,polar + S unpolor è S 0,polar = S max - S unpolar = = 6.0 W/m 2

8 Polarization and the Reflection and Refraction of Light θ p θ p Reflected light is 100% horizontally polarized at the polarizing angle, θ p Brewster s law tanθ p = n 2 n 1 For air/water interface: # n 1 =1.00, n 2 =1.33 θ p = tan & % ( = 53.1 o $ 1.00 ' )( 1.00)sin53.1 o, n 1 sinθ p = n 2 sinθ 2 θ 2 = sin 1 +. = 36.9 o * θ p +θ 2 = 90 o à Always true at θ p

9 Chapter 25 Optical Instruments and the Eye

10 Cameras IMAGE FORMATION BY A CONVERGING LENS IN A CAMERA When the object is placed further than twice the focal length from the camera lens, the real image is inverted and smaller than the object on the film or ccd chip.

11 Cameras Example: Taking a picture of a flower vase with a ccd camera. A m high flower vase is positioned 2.00 m in front of a ccd camera. The camera uses a converging lens whose focal length is 60.0 mm. (a) How far must the ccd be from the lens to have a sharp image? (b) Find the height of the image on the ccd. (c) If the lens diameter is 3.0 cm, find the f-stop of the lens. (d) If a properly exposed picture is taken with this f-stop with a shutter speed of 1/500 s, what f-stop is needed for a shutter speed of 1/125 s so that the picture is not overexposed? (a) (b) 1 d i = 1 f 1 d o = m m d i = m = 61.9 mm h i = d i h o = d o 2.00 =16.17 m = m = 15.5 mm

12 (c) f stop = = f Diameter of lens opening = f D 60 mm 30 mm = 2.0 f / 2 (d) For the picture not to be overexposed, we must reduce the lens area by the ratio of the shutter speeds, i.e. A final = A initial = 1 4 A initial! π D $ final # & " 2 % 2 f stop final = = 1 4 π! D $ initial # & " 2 % f D final = 2 2 D final = 1 2 D initial f D initial = ( ) = 4.0 f / 4

13 The Human Eye ANATOMY

14 The Human Eye OPTICS The lens only contributes about 20-25% of the refraction, but its function is important. Normal eye near point, i.e. nearest point for comfortable focusing, N = 25 cm Normal eye far point, i.e. farthest point for comfortable focusing à

15 The Human Eye NEARSIGHTEDNESS The lens creates an image of the distance object at the far point of the nearsighted eye.

16 The Human Eye Example: Eyeglasses for the Nearsighted Person A nearsighted person has a far point and near point located at only 10.0 cm and 8.0 cm, respectively, from the eye. Assuming that eyeglasses are to be worn 2.0 cm in front of the eye, find (a) the focal length needed for the lens of the glasses so the person can see distant objects and (b) the resulting location of the near point when the person is wearing these glasses.

17 The Human Eye (a) d o =, d i = ( ) = 8.0 cm 1 f = = 1 d o d i ( ) = cm We want a virtual, upright image at the person s far point f = 8.0 cm f < 0, diverging lens (b) d i = ( ) = 6.0 cm 1 d o = 1 f 1 d i = 1 ( 8.0) 1 ( 6.0) We want a virtual, upright image at the person s near point = cm 1 d o = 24.0 cm N = = 26.0 cm Close to the normal near point of 25 cm

18 The Human Eye FARSIGHTEDNESS The lens creates an image of the close object at the near point of the farsighted eye.

19 Example: Eyeglasses for the Farsighted Person A farsighted person has a near point located at 75.0 cm. from the eye. Assuming that eyeglasses are to be worn 2.0 cm in front of the eye, find the focal length needed for the lens of the glasses so the person s near point with glasses is 25.0 cm.

20 d o = = 23.0 cm, d i = ( ) = 73.0 cm 1 f = = 1 d o d i ( ) = cm 1 We want a virtual, upright image at the person s near point f = 33.6 cm f > 0, converging lens

21 The Human Eye THE REFRACTIVE POWER OF A LENS THE DIOPTER Optometrists who prescribe correctional lenses and the opticians who make the lenses do not specify the focal length. Instead they use the concept of refractive power. Refractive power (in diopters) = f 1 ( in meters)

22 Example: What refractive power, in diopters, would the optometrist prescribe for the lenses found in the last two examples, i.e. nearsighted and farsighted? Refractive power (in diopters) = P = Nearsighted example : f = 8.0 cm = m P = 1 f = 1 ( 0.080) = 12.5 D 1 f in meters ( ) Farsighted example : f = 33.6 cm = m P = 1 f = = D

23 Angular Magnification and the Magnifying Glass The size of the image on the retina determines how large an object appears to be.

24 Angular Magnification and the Magnifying Glass θ ( in radians) = Angular size h d o o

25 Angular Magnification and the Magnifying Glass Example: A Penny and the Moon Compare the angular size of a penny held at arms length with that of the moon. Penny θ h d o o = 1.9 cm 71cm = rad Moon θ h d o o = m m = rad

26 Angular Magnification and the Magnifying Glass Angular magnification M = θʹ θ θ ' h o d o, M h o h o θ h o N d o N = N # = N 1 d o f 1 & % ( $ d i ' Special cases: Relaxed focus % d i = M N ' 1 f 1 & Focus at N ( ) % d i = N M N ' 1 f 1 & N ( ) ( * = N ) f ( * = N ) f +1

27 Example of a magnifying glass: A magnifying glass has a focal length of 9.5 cm. Find the magnification of the lens when used (a) with a relaxed eye, and (b) with the image at N=25 cm. f = 9.5 cm (a) M N f = = 2.6 times ( d o = f = 9.5 cm) (b) M N f 25 +1= = 3.6 times ( d o = 6.9 cm)