MR. SURRETTE VAN NUYS HIGH SCHOOL
CHAPTER 15:
REFLECTION AND REFRACTION
WORKSHEET SOLUTIONS
1. Light in air enters a diamond (n = 2.42) at an angle of incidence of 30.0o. What is the angle of refraction inside the diamond?
1A.
(1) n = sinq1 / sinq2
(2) sinq2 = sinq1 / n
(3) sinq2 = sin 30o / 2.42
(4) sinq2 = 0.2066
(5) q2 = arcsinq2 = 11.9o
2. An underwater scuba diver sees the sun at an apparent angle of 35.0o from the vertical. How far is the sun above the horizon? (nwater = 1.33)
2A.
(1) n = sinq2 / sinq1
(2) (n)(sinq1) = sinq2
(3) (1.33)(sin 35o) = sinq2
(4) sinq2 = 0.763
(5) q2 = arcsinq2 = 49.7o
3. Dispersion occurs when:
(A) some materials bend light more than other materials
(B) a material slows down some wavelengths more than others
(C) a material changes some frequencies more than others
(D) light has different speeds in different materials
(E) a material changes the color of incoming light
4. If the velocity of light through an unknown liquid is measured at 1.85 x 108 m/s, what is the index of refraction of this liquid?
4A.
(1) n = c / v
(2) n = 3.00 x 108 m/s / 1.85 x 108 m/s
(3) n = 1.62
5. If the critical angle for internal reflection inside a certain transparent material is found to be 56.0o, what is the index of refraction of the material? (Air is outside the material).
5A.
(1) sin qc = n2 / n1
(2) n1 = n2 / sinqc
(3) n1 = 1.00 / sin 56o
(4) n1 = 1.21
6. Which of the following describes what will happen to a light ray incident on an air-to-glass boundary at less than the critical angle?
(A) total reflection
(B) total transmission
(C) total dispersion
(D) partial reflection, total transmission
(E) partial reflection, partial transmission
6A.
7. A beam of light in air is incident at an angle of 35.0o to the surface of a rectangular block of clear plastic (n = 1.49). The light beam first passes through the block and re-emerges from the opposite side into air at what angle to the surface?
Example 7. Diagram
7A. 35o
8. A beam of light in air is incident on the surface of a rectangular block of clear plastic
(n = 1.49). If the velocity of the beam before it enters the plastic is 3.00 x 108 m/s, what is its velocity after emerging from the block?
8A. 3.00 x 108 m/s
9. A ray of light in air is incident on an air-to-glass boundary at an angle of 41.5o with the normal. If the index of refraction of the glass is 1.47, what is the angle of the refracted ray within the glass with respect to the normal?
9A.
(1) n = sinq1 / sinq2
(2) sinq2 = sinq1 / n
(3) sinq2 = sin 41.5o / 1.47
(4) sinq2 = 0.451
(5) q2 = arcsinq2 = 26.8o
10. A light in air is incident on an air-to-glass boundary at an angle of 45.0o and is refracted in the glass at an angle of 30.0o with the normal. What is the index of refraction of the glass?
10A.
(1) n = sinq1 / sinq2
(2) n = sin 45o / sin 30o
(3) n = 0.707 / 0.5
(4) n = 1.41
11. A laser beam, incident at 30 degrees onto the surface of a block of glass, is partially reflected and partially transmitted (with refraction) at the block’s upper surface. The index of refraction of the glass is 1.5.
Example 11. Diagram
11a. What is the speed of light in the glass expressed as a fraction of c?
A.
(1) n = c / v
(2) v = c / n
(3) v = (1 c) / (1.5)
(4) v = 0.67 c
11b. Is the angle of refraction greater than, less than, or equal to 30 degrees?
A. less than
11c. Calculate the angle of refraction in degrees.
A.
(1) n1sinq1 = n2sinq2
(2) sinq2 = (n1)(sinq1) / (n2)
(3) sinq2 = (1.0)(sin30o) / (1.5)
(4) sinq2 = 0.333
(5) q2 = arcsinq2 = 19.5o
11d. What is the angle the reflected beam makes with the normal?
A. 30 degrees. The angle of reflection = the angle of incidence.
12. A beam of light in water strikes a boundary with air. The index of refraction of water is 1.33.
12a. If the angle of incidence is 41 degrees what is the angle of refraction?
A.
(1) n1 sin q1 = n2 sin q2
(2) sinq2 = (n1)(sin q1) / (n2)
(3) sinq2 = (1.33)(sin 41o) / (1.00)
(4) sinq2 = 0.873
(5) q2 = arcsinq2 = 60.8o
12b. Calculate the critical angle for these rays.
A.
(1) n1sinq1 = n2sinq2
(2) sinq1 = (n2)(sinq2) / (n1)
(3) sinq1 = (1.00)(sin 90o) / (1.33)
(4) sinq1 = 0.752
(5) q1 = arcsinq1 = 48.8o
12c. If the angle of incidence is 61 degrees what happens to the light at the boundary?
A. It is totally reflected.
CHAPTER 16: OPTICS
WORKSHEET SOLUTIONS
1. Which of the following best describes the image of a concave mirror when the object is at a distance greater than twice the focal point from the mirror?
(A) virtual, erect; and magnification greater than one
(B) virtual, inverted; and magnification greater than one
(C) real, inverted; and magnification less than one
(D) virtual, erect; and magnification less than one
(E) real, inverted; and magnification greater than one
1A. (C) real, inverted; and magnification less than one
2. If a man’s face is 25.0 cm in front of a concave shaving mirror creating an erect image 2.25 times as large as the object, what is the object’s focal length?
2A.
(1) M = - si / so
(2) - si = M(so)
(3) si = - (2.25)(25.0 cm)
(4) si = - 56.25 cm
(5) 1/so - 1/si = 1/f
(6) 1/f = 1/ 25 cm – 1/ 56.25 cm
(7) 1/f = 0.0400 cm – 0.0178 cm
(8) 1/f = 0.0222 cm
(9) f = 45 cm
3. An object is placed at a distance of 35.0 cm from a thin lens along an axis. If a virtual image forms at a distance of 70.0 cm from the lens, on the same side of the object, what is the focal length of the lens?
3A.
(1) 1/ so – 1/ si = 1/ f
(2) 1/ 35cm – 1/ 70cm = 1/ f
(3) 1/ f = 2/ 70cm – 1 /70cm
(4) 1/ f = 1/ 70cm
(5) f = 70 cm
4. Two thin lenses of focal lengths 15.0 and 20.0 cm, respectively, are placed in contact so that their optic axes coincide. What is the focal length of the two in combination?
4A.
(1) 1/ f1 +1/ f2 = 1/ fS
(2) 1/ 15cm + 1/ 20cm = 1/ fS
(3) 4/ 60cm + 3/ 60cm = 1/ fS
(4) 7/ 60cm = 1/ fS
(5) fS = 60cm/ 7 = 8.6 cm
Questions 5 - 7. A concave spherical mirror has a radius of curvature of 24 cm. An object is placed 32 cm from the mirror’s vertex.
5. What is the focal length of this mirror?
5A.
(1) f = R / 2
(2) f = 24 cm / 2
(3) f = 12 cm
6. Sketch a ray diagram.
6A.
7. Calculate the image distance and describe the image.
7A.
(1) 1/ f = 1/ so + 1 /si
(2) 1/ si = 1/ f – 1 /so
(3) 1/ si = 1/ 12cm – 1 / 36cm
(4) 1/ si = 3/ 36cm – 1/ 36cm
(5) 1/ si = 2/ 36 cm = 1/ 18 cm
(6) si = 18 cm (inverted)
8. A concave spherical mirror has a radius of curvature of 30 cm. An object is placed 12 cm from the mirror’s vertex. Sketch a ray diagram.
8A.
9. A double-convex lens has a 20 cm radius of curvature for both sides. An object is placed 7 cm from the mirror’s vertex on the left-hand side. Sketch a ray diagram.
9A.
10. A Young’s double slit apparatus has a slit separation of 4.75 x 10-5 m on which a monochromatic light beam is directed. The resultant bright fringes on a screen 1.30 m away are separated by
1.75 x 10-2 m. What is the wavelength of the beam?
10A.
(1) xm = mlL / d
(2) l = dxm / mL
(3) l = [(4.75 x 10-5 m)(1.75 x 10-2 m)] / [(1)(1.30 m)]
(4) l = 6.39 x 10-7 m
(5) l = 639 nm
11. Constructive interference occurs when light of wavelength 565 nm shines on soap bubble film (n = 1.46). What is the minimum thickness of the film?
11A.
(1) 2nt = (m + ½)l
(2) 2nt = (m + ½)l
(3) 2nt = ½ l
(4) 4nt = l
(5) t = l / 4n
(6) t = (565 x 10-9 m) / (4)(1.46)
(7) t = 9.67 x 10-8 m
12. A beam of unpolarized light strikes a flat piece of glass at an incidence angle of 49.5o. If the reflected beam is completely polarized, what is the glass’ index of refraction?
12A.
(1) n = tan qp
(2) n = tan (49.5o)
(3) n = 1.17
13. In a Young’s double-slit experiment, by what factor is the distance between adjacent light and dark fringes changed when the wavelength of the source is tripled?
13A.
(1) xm = mlL / d
(2) xm = m(3l)L / d
(3) xm = 3 [mlL / d]
14. A possible means for making an airplane radar-invisible is to coat the plane with an anti-reflective polymer. If radar waves have a wavelength of 2.25 cm and the index of refraction of the polymer is n = 1.62, how thick would the coating be?
14A.
(1) 2nt = (m + ½)l
(2) 2nt = (m + ½)l
(3) 2nt = ½ l
(4) 4nt = l
(5) t = l / 4n
(6) t = (2.25 x 10-2 m) / (4)(1.62)
(7) t = 3.47 mm
Questions 15 - 16. Light in the form of plane waves of a single wavelength are incident on two parallel slits. A viewing screen is a distance D from the slits. A point P on the screen is a distance r1 from one slit and r2 from the other.
Questions 15 - 16. Diagram
15. If the difference in the distances (r2 – r1) is 1.5 wavelengths (3l/2) what would be observed at P?
A. A minimum. Destructive interference occurs when the extra distance is an odd integer multiple of the wavelength divided by 2.
16. If the difference in the distances (r2 – r1) is 2.0 wavelengths (2l) what would be observed at P?
A. A maximum. Constructive interference.
CHAPTER 16: OPTICS
MIRRORS, LENSES, AND WAVE OPTICS
QUIZ SOLUTIONS
1. If a man’s face is 25.0 cm in front of a concave shaving mirror creating an erect image 3.00 times as large as the object, what is the object’s focal length?
1A.
(1) M = - si / so
(2) - si = M(so)
(3) si = - (3.00)(25.0 cm)
(4) si = - 75.0 cm
(5) 1/so - 1/si = 1/f
(6) 1/f = 1/25cm – 1/75cm
(7) 1/f = 3/75cm – 1/75cm
(8) 1/f = 2/75cm
(9) f = 75/2 cm
(10) f = 37.5 cm
2. An object is placed at a distance of 32.0 cm from a thin lens along an axis. If a virtual image forms at a distance of 64.0 cm from the lens, on the same side of the object, what is the focal length of the lens?
2A.
(1) 1/so – 1/si = 1/f
(2) 1/32cm – 1/64cm = 1/f
(3) 1/f = 2/64cm – 1/64cm
(4) 1/f = 1/64cm
(5) f = 64.0 cm
3. Two thin lenses of focal lengths 12.0 and 18.0 cm, respectively, are placed in contact so that their optic axes coincide. What is the focal length of the two in combination?
3A.
(1) 1/f1 +1/f2 = 1/fS
(2) 1/12cm + 1/18cm = 1/fS
(3) 1/fT = 3/36cm + 2/36cm
(4) 1/fS = 5/36cm
(5) fS = 36/5 cm
(6) fS = 7.2 cm
Questions 4 - 6. A concave spherical mirror has a radius of curvature of 30 cm. An object is placed 60 cm from the mirror’s vertex.
4. What is the focal length of this mirror?
4A.
(1) f = R / 2
(2) f = 30cm / 2
(3) f = 15 cm
5. Sketch a ray diagram.
5A.
6. Calculate the image distance and describe the image.
6A.
(1) 1/f = 1/so + 1/si
(2) 1/si = 1/f – 1/so
(3) 1/si = 1/15cm – 1/60cm
(4) 1/si = 4/60cm – 1/60cm
(5) 1/si = 3/60cm
(6) 1/si = 1/20cm
(7) si = 20 cm (inverted)
7. A Young’s double slit apparatus has a slit separation of 3.25 x 10-5 m on which a monochromatic light beam is directed. The resultant bright fringes on a screen 2.15 m away are separated by 3.45 x 10-2 m. What is the wavelength of the beam?