Consider unpolarized sunlight incident on water. The reflectedlightis partially poarized parallel to the water surface as shownbelow.At some angle of incidence, called the Brewster angle, allof thereflected light is polarized parallel to the surface of thewater.How would you design a pair of sunglasses using polaroidfilm suchthat they significantly reduce the intensity of reflectedlightreaching the eyes?

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Unpolarized light in air is incident on a body ofwater (nw = 1.33) such that the reflected light iscompletely linearly polarized.

(a) What is the angle of incidence?

(b) The transmitted light hits a block of glass(ng = 1.5) located some distance under the surface of thewater. Again, the light reflected from the glass is completelylinearly polarized. What is the angle between the water and glasssurfaces?

(c) Imagine that instead of hitting a single blockof glass, the light transmitted into the water hits a stack glassplates (oriented at the angle found in Part (b)) separated by thinlayers of water. Calculate the number of plates necessary to giverise to a polarization extinction ratio of 20 dB (in intensity) atthe output.

DUE DATE: 12 00 noon Monday. Dec 6. 2010. The problems on this assignment are quite word because strong direction is being given to Students in how to proceed. Two problems will be selected at random for marking. Percentage polarization. It is useful to characterize partially polarized light in terms of its "percentage polarization". A light beam of constant intensity Io. is allowed to fall at normal incidence on an "ideal linear polarizer" (a linear polarizer is "ideal" if it panes all light polarized parallel to the polarizer's axis, and stops all light polarized perpendicular to that axis.) As the ideal polarizer is rotated continuously (see Figure 8.1; about an axis perpendicular to its plane, the transmitted intensity I passes through successive maximum and minimum values (denoted by I max and I min). The percentage polarization of the incident light is denned to be Find the percentage polarization measured in this way for the following light beams: "Unpolarized natural light" tor which I max = I min = Io/2. A beam of light. Initially unpolarixed. that has been passed through an ideal linear polarizer before being measured for percentage polarization. A beam of light, initially unpolarizcd, that has been passed through a non-ideal polarizer that (in terms of light intensity) transmits 70% of light polarized parallel to its polarizing axis and 20% of light polarized perpendicular to its polarizing axis. Circularly polarized light. (Circular polarization means that at any given fixed observation point In the beam, the E-vector has constant magnitude but rotates at the frequency of the electric field oscillations so that the tip of the vector describes a circle in the zy plane (perpendicular to the light ray at the point in question). Elliptically polarized light for which the tip of the E-vector moves on an ellipse in the x y plane, defined by where Ax and Ay are the amplitudes of the oscillating Ex and E y components of the electric field vector, and is the phase difference between those oscillations. NOTE: Do your calculation for the special case Ax = 2Ay and e =pi / 2. [(8.2) taxes a particularly simple form when e = pi / 2.]

If a virtual image is formed 9.0 cm along the principal axis from aconvex mirror of focal length â15.0 cm, how far is the object fromthe mirror?

2. A woman looking in a makeup mirror sees her face at twice itsactual size and right-side up. If she is 26.0 cm from the mirror,what is its focal length?

3. Which of the following best describes the image of a concavemirror when the object is at a distance greater than twice thefocal point distance from the mirror?
a. virtual, upright and magnification greater than one
b. real, inverted and magnification less than one
c. virtual, upright and magnification less than one
d. real, inverted and magnification greater than one

4. A convex mirror with focal length of ?18 cm forms an image 12 cmbehind the surface. Where is the object located as measured fromthe surface?

5. A convex mirror with a focal length of ?18 cm forms an image 15cm behind the surface. If the object height is 1.2 cm what is theimage height?

6. An object placed 14 cm from a concave mirror produces a realimage 8.0 cm from the mirror. If the object is now moved to a newposition 18.0 cm from the mirror, where is the new image located asmeasured from the mirror?

7. When the reflection of an object is seen in a concave mirror theimage will:

8. A candle is 40.0 cm in front of a convex spherical mirror ofradius of curvature 70.0 cm. What are the image distance and themagnification, respectively?

9. An object is 16.0 cm from the surface of a spherical Christmastree ornament that is 8.00 cm in diameter. What is themagnification of the image?

10. A solid glass sphere with a radius of 6.00 cm and index ofrefraction of 1.50 has a small coin embedded 3.00 cm from the frontsurface of the sphere. For the viewer looking at the coin throughthe glass, at what distance from the front surface of the glassdoes the coinâs image appear to be located?

11. A glass block, for which n = 1.52, has a blemish located 4.5 cmfrom one surface. At what distance from that surface does the imageof the blemish appear to the outside observer?

12. An object of length 2.00 cm is inside a plastic block withindex of refraction 1.50. If the object is viewed from directlyabove, what is the length of its image?

13. An object is placed at a distance of 25 cm from a thin convexlens along its axis. The lens has a focal length of 10 cm. What arethe values, respectively, of the image distance andmagnification?
14. An object is placed at a distance of 50 cm from a thin lensalong the axis. If a real image forms at a distance of 35 cm fromthe lens, on the opposite side from the object, what is the focallength of the lens?

15. A contact lens is made of plastic with an index of refraction1.50. The lens has an outer radius of curvature of +2.0 cm and aninner radius of curvature of +2.5 cm. What is its focallength?

16. A Youngâs double slit has a slit separation of 2.50 ? 10?5 m onwhich a monochromatic light beam is directed. The resultant brightfringes on a screen 2.00 m from the double slit are separated by2.30 ? 10?2 m. What is the wavelength of this beam? (1 nm = 10?9m)

17. A Youngâs double-slit apparatus is set up so that a screen ispositioned 1.9 m from the double slits, and the spacing between thetwo slits is 0.040 mm. What is the distance between alternatingbright fringes on the screen if the light source has a wavelengthof 630 nm? (1 nm = 10?9 m)

18. The blue tint of a coated camera lens is largely caused by whateffects?

19. What is the minimum thickness of a glycerin film (n = 1.47) onwhich light of wavelength 650 nm shines that results inconstructive interference of the reflected light? Assume the filmis surrounded front and back by air.

20. Light of wavelength 560 nm is incident on a slit of width 0.150mm, and a diffraction pattern is produced on a screen that is 2.00m from the slit. What is the width of the central bright fringe? (1nm = 10?9 m)

21. Light of wavelength 610 nm is incident on a slit of width 0.25mm, and a diffraction pattern is produced on a screen that is 1.5 mfrom the slit. What is the distance of the second dark fringe fromthe center of the bright fringe? (1 nm = 10?9 m)

22. A multiple slit diffraction grating has a slit separation of2.50 ? 10?6 m. Find the wavelength of the monochromatic light thatwill have its second order bright fringe diffracted through anangle of 38.0Â°. (1 nm = 10?9 m)

23. A diffraction grating with 12 000 lines/cm will exhibit thefirst order maximum for light of wavelength 510 nm at what angle?(1 nm = 10?9 m)

24. A beam of unpolarized light in air strikes a flat piece ofglass at an angle of incidence of 58.0Â°. If the reflected beam iscompletely polarized, what is the index of refraction of theglass?

25. A beam of polarized light of intensity I0 passes through asheet of ideal polarizing material. The polarization axis of thebeam and the transmission axis of the sheet differ by 45Â°. What isthe intensity of the emerging light?

26. At what angle is the sun above the horizon if its light isfound to be completely polarized when it is reflected from the topsurface of a slab of glass (n = 1.65)?

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