PHYS 102 Chapter Notes - Chapter 23: Curved Mirror, Plane Mirror, Refraction

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Light appears to travel in straight-line paths, called rays, at a speed that depends on the index of refraction, (cid:1866), of the material; that is: (cid:1866)=(cid:1855) Where (cid:1855) is the speed of light in a vacuum. When light reflects from a flat surface, the angle of reflection equals the angle of incidence. This law of reflection explains why mirrors can form images. In a plane mirror, the image is virtual, upright, the same size as the object, and is as far behind the mirror as the object is in front. A spherical mirror can be concave or convex. A concave spherical mirror focuses parallel rays of light (light from a very distant object) to a point called the focal point. The distance of this point from the mirror is the focal length of the mirror and: Where is the radius of curvature of the mirror.

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In many cars, the passenger's side mirror has the following warning "Objects in mirror are closer than they appear" embossed on the mirror surface. Your group decides to conduct the following experiment to verify this statement. One member of your group holds a plane mirror just below the passenger's side mirror (radius of curvature =1.60 m) so that you can view an 8.4-cm tall object 2.4 m away from both mirrors. By placing a small ruler on the surface of each mirror, you find that the object appears to be 2.10cm tall in the plane mirror and 1.20cm tall in the passenger's side mirror when you view the images at a distance of .80m in front of the mirrors. Are the images real or virtual? Is the passenger's side mirror concave or convex? Show why the image in the passenger's side mirror appears to be farther away than the object actually is or as viewed on the plane mirror. (Hint:Draw a ray diagram of the object, image, mirror, and your eye for each mirror so that you have a better idea of what your eyes see i.e. the apparent angular size of the image and the corresponding apparent distance away as seen by your eye for both mirrors)

1) On the plane mirror system shown here, if thefinalangle
of reflection for this ray is 14.0Â°, find the initial angleofincidence.

A ray oflight is sent between parallel planemirrors, as shown.The raybarely misses the lower mirror as itenters theâcorridor.â The mirrors' edges are aligned withoneanother, as shown. The mirrors are 3.00 cm apart, and each is18.0cm long. Find the smallest initial angle of incidence so thattherayâ¦
(i)hits only the topmirror.
(ii)hits each mirror exactly once.

3) Why don't diamonds sparkle as much when viewedunderwater?Explain thoroughly,using words, equations and diagramsasnecessary.

4) A spherical mirror producesan image that is located 43.0 cmbehind the mirror when the objectis located 12.5 cm in front ofthemirror.

(i)What is the focal length ofthemirror? (ii)Isthis mirror concave orconvex?

5)A concave mirror (f= 54.0 cm) produces a real imagewhose distance from themirror is one-third of theobjectdistance. (i)Findtheobjectdistance. (ii)Findthe imagedistance.

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)?

PHYS 102 Chapter Notes - Chapter 23: Curved Mirror, Plane Mirror, Refraction

PHYS 102 Full Course Notes

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