Reflection - AP Physics 2

1. A plane mirror is mounted vertically. A light ray approaches from the left, making $50^\circ$ with the normal, and reflects back into the left side. What is the reflected angle relative to the normal?
   Answer: $50^\circ$ This question tests understanding of reflection. According to the law of reflection, when a light ray strikes a mirror, the angle of incidence equals the angle of reflection, both measured from the normal. Since the incident ray makes 50° with the normal, the reflected ray must also make 50° with the normal. The fact that the mirror is vertical and the light reflects "back into the left side" simply means the reflected ray is on the opposite side of the normal from the incident ray. Choice A (40°) represents a common error of subtracting 10° for no physical reason. Remember that reflection follows a simple rule: the angle in equals the angle out, always measured from the normal line perpendicular to the surface.
2. A ray of light in air reflects from a flat mirror. The incident ray travels up and to the right at $48^\circ$ to the mirror surface; the reflected ray travels up and to the left. The reflected ray makes which angle with the normal?
   Answer: $42^\circ$ This question tests understanding of reflection angle calculations when given the angle to the surface. If the incident ray makes 48° with the mirror surface, it makes 90° - 48° = 42° with the normal (since the normal is perpendicular to the surface). By the law of reflection, the reflected ray must also make 42° with the normal. Choice A (48°) incorrectly uses the angle to the surface as the angle to the normal, failing to recognize that these are complementary angles. When given an angle to the surface, first convert it to the angle from the normal by subtracting from 90°, then apply the law of reflection.
3. A water wavefront strikes a straight, rigid barrier and reflects. The incident wave travels toward the barrier at an angle to the normal, and the reflected wave travels away on the other side of the normal. Which statement correctly describes the reflection?
   Answer: The reflected wavefront makes the same angle to the normal as the incident wavefront. This question tests understanding of reflection of water waves. The law of reflection applies to all wave types: the angle of incidence equals the angle of reflection, with both angles measured from the normal to the reflecting surface. When a water wavefront strikes a barrier at an angle, the reflected wavefront makes the same angle with the normal as the incident wavefront, traveling on the opposite side of the normal. Choice A incorrectly refers to angles measured from the barrier rather than the normal, a common misconception that leads to incorrect angle relationships. For any wave reflection, establish the normal (perpendicular to the barrier) and measure all angles from it.
4. A ray of light reflects from a plane mirror. The incident ray makes $60^\circ$ with the normal; the reflected ray leaves on the other side of the normal. What is the angle between the incident and reflected rays?
   Answer: $120^\circ$ This question tests understanding of reflection. By the law of reflection, when the incident ray makes 60° with the normal, the reflected ray also makes 60° with the normal on the opposite side. The angle between the incident and reflected rays equals the sum of these two angles: 60° + 60° = 120°. The normal bisects the angle between the incident and reflected rays. Choice A (60°) represents only one of the angles to the normal, not the total angle between the rays—a common error when visualizing reflection geometry. To find the angle between incident and reflected rays, add both angles to the normal: 2θi.
5. A narrow light ray strikes a flat mirror in air. The incident ray approaches the mirror at $35^\circ$ to the normal; the reflected ray leaves on the opposite side of the normal. Which statement correctly describes the reflection?
   Answer: The reflected angle equals $35^\circ$ measured from the normal. This question tests understanding of reflection. The law of reflection states that when a light ray strikes a smooth surface, the angle of incidence equals the angle of reflection, with both angles measured from the normal (a line perpendicular to the surface at the point of incidence). Since the incident ray approaches at 35° to the normal, the reflected ray must also make 35° with the normal, but on the opposite side. The reflected angle does not depend on the mirror material or whether light "slows" near the mirror - these are common misconceptions that confuse reflection with refraction. Choice B incorrectly suggests that light speed affects the reflection angle, which only applies to refraction between different media. When solving reflection problems, always identify the normal first and measure all angles from this reference line, not from the surface itself.
6. A plane mirror is rotated by $10^\circ$ while a fixed incident laser beam continues to strike it. The incident direction is unchanged, and the reflected direction shifts accordingly. By how much does the reflected ray direction rotate?
   Answer: $20^\circ$ This question tests understanding of reflection. When a plane mirror rotates by an angle θ, the reflected ray rotates by 2θ. This occurs because rotating the mirror changes the normal direction by θ, which affects both the incident and reflected angles equally. Since the incident beam direction is fixed, the incident angle relative to the new normal changes by θ, and by the law of reflection, the reflected angle also changes by θ in the same rotational sense. The total angular change of the reflected ray is θ + θ = 2θ. For a 10° mirror rotation, the reflected ray rotates by 20°. Choice A (10°) represents the common misconception that the ray rotation equals the mirror rotation. Always remember: mirror rotation causes double the angular deviation in the reflected beam.
7. A ray of light reflects from a smooth mirror. The incident direction is in the plane of the page and makes an angle $\theta_i$ with the normal. The reflected direction also remains in that plane. Which statement correctly describes the reflection?
   Answer: $\theta_r=\theta_i$ because reflection is specular from a smooth surface This question tests understanding of reflection. For specular (mirror-like) reflection from a smooth surface, the law of reflection states that θr = θi, where both angles are measured from the normal to the surface. This relationship is purely geometric and does not depend on material properties like reflectivity or the speed of light in different media. Choice C (θr = 90° - θi) represents a common misconception of measuring one angle from the surface while measuring the other from the normal. To avoid confusion, always consistently measure both incident and reflected angles from the normal, never from the surface.
8. A light ray in air reflects from a flat mirror. The incident direction makes $20^\circ$ with the mirror surface (not the normal). The reflected direction leaves on the other side of the normal. What is the reflected angle measured from the normal?
   Answer: $70^\circ$ This question tests understanding of reflection. The law of reflection requires that incident and reflected angles be measured from the normal, not from the surface. If the incident ray makes 20° with the mirror surface, it makes 90° - 20° = 70° with the normal. By the law of reflection, the reflected ray also makes 70° with the normal on the opposite side. Choice A (20°) represents the misconception of directly using the surface angle instead of converting to the normal angle. When working with reflection problems, always convert surface angles to normal angles using the complementary relationship: angle from normal = 90° - angle from surface.
9. Plane wavefronts of light in air approach a flat mirror. The incident direction is $20^\circ$ above the surface (grazing), and the reflected direction returns into air. Which statement correctly describes the reflection?
   Answer: The reflected direction is $20^\circ$ above the surface on the other side of the normal. This question tests understanding of reflection. The law of reflection applies to all waves, including light wavefronts: the angle of incidence equals the angle of reflection, both measured from the normal. If the incident direction is 20° above the surface (grazing angle), then it makes 70° with the normal (since 90° - 20° = 70°). By the law of reflection, the reflected direction also makes 70° with the normal, which means it's 20° above the surface on the opposite side of the normal. Choice B incorrectly states 70° above the surface, confusing the angle from the normal with the angle from the surface. When given grazing angles, convert to normal angles first: grazing angle + normal angle = 90°.
10. A light ray reflects from a smooth surface. The incident ray approaches making $15^\circ$ with the normal; the reflected ray leaves on the opposite side of the normal. Which statement correctly describes the reflection?
    Answer: The reflected angle is $15^\circ$ when measured from the normal. This question tests understanding of reflection. According to the law of reflection, when the incident ray approaches at 15° from the normal, the reflected ray must leave at 15° from the normal on the opposite side. This angle relationship is independent of surface color, material properties, or the size of the angle. Choice A incorrectly measures from the surface instead of the normal - if the ray makes 15° with the normal, it makes 75° with the surface, but we always use normal angles for the reflection law. The fundamental principle to remember is that reflection angles are always measured from the normal, and the angle in equals the angle out.
11. A light ray in air hits a smooth, horizontal mirror. The incident ray travels downward-right; the reflected ray travels upward-right. Which statement correctly describes the reflection?
    Answer: The reflected angle equals the incident angle, both measured from the normal. This question tests understanding of reflection. The law of reflection applies universally to all smooth surfaces: the angle of incidence equals the angle of reflection, with both angles measured from the normal line. When a light ray travels "downward-right" and reflects to travel "upward-right," it maintains the same angle with the normal on both sides. The reflection angle does not depend on the mirror's temperature, orientation, or material properties like the speed of light within it. Choice D incorrectly suggests that the mirror material affects the reflection angle, confusing this with refraction where material properties do matter. To correctly analyze reflection problems, always draw the normal at the point of incidence and measure angles from this perpendicular reference line.
12. A light ray reflects from a flat mirror in air. The incident ray is at $30^\circ$ to the normal, producing a reflected ray. If the light's frequency increases while the incident direction stays the same, what happens to the reflected angle?
    Answer: It stays the same because $\theta_r=\theta_i$. This question tests understanding of reflection. The law of reflection (angle of incidence equals angle of reflection) is independent of the light's frequency, wavelength, or color—it depends only on the geometry of the incident ray and surface. When the incident ray is at 30° to the normal, the reflected ray is also at 30° to the normal, regardless of frequency. All electromagnetic waves follow the same reflection law. Choice B incorrectly suggests frequency affects reflection angle, possibly confusing reflection with dispersion effects in refraction. Remember: reflection is a purely geometric phenomenon—frequency changes neither the incident nor reflected angles.
13. A water wavefront approaches a straight vertical seawall at an angle. The incident wavefronts are evenly spaced, and the reflected wavefronts move away from the wall on the other side of the normal. Which statement correctly describes the reflection?
    Answer: The reflected wavefront spacing equals the incident spacing. This question tests understanding of reflection. When water waves reflect from a vertical seawall, the law of reflection applies: the angle of incidence equals the angle of reflection, measured from the normal to the wall. The wavelength (and thus wavefront spacing) remains constant during reflection because the wave stays in the same medium (water) with the same frequency and speed. The reflected wavefronts maintain their original spacing but travel in a new direction determined by the reflection angle. The wave energy is redirected, not added to or removed. Choice B incorrectly suggests the wall adds energy to increase spacing, but walls only redirect waves without changing their properties in the same medium. When analyzing wave reflection, remember that frequency, wavelength, and speed remain constant in the same medium.
14. A light ray reflects from a plane mirror submerged in water. The incident direction in water makes $30^\circ$ with the normal to the mirror. The reflected direction remains in water. Which statement correctly describes the reflection?
    Answer: The reflected angle equals $30^\circ$ measured from the normal This question tests understanding of reflection. The law of reflection applies within any uniform medium, including water. When light traveling in water reflects from a mirror, the incident and reflected angles remain equal when measured from the normal, regardless of the medium. Since the incident angle is 30° from the normal, the reflected angle is also 30° from the normal. Choice B incorrectly suggests the angle changes due to light speed in water, confusing reflection with refraction at medium boundaries. Remember that reflection follows the same geometric law in any medium - the key is that both incident and reflected rays stay in the same medium.
15. A pulse on a rope travels rightward toward a rigid wall. The incident pulse is upright, and the reflected pulse travels leftward. Which statement correctly describes the reflection?
    Answer: The reflected pulse is inverted relative to the incident pulse. This question tests understanding of reflection. When a wave pulse on a rope reflects from a rigid (fixed) boundary like a wall, the reflected pulse is inverted relative to the incident pulse. This inversion occurs because the wall exerts an equal and opposite force on the rope, creating a reflected pulse with opposite displacement. An upright incident pulse becomes an inverted (downward) reflected pulse traveling in the opposite direction. The pulse maintains the same speed in the same medium but reverses direction. Choice B incorrectly assumes rigid walls prevent inversion, when actually rigid boundaries cause inversion while free boundaries preserve orientation. To remember this principle, think of the wall as pushing back with an opposite force, creating the inverted reflection.
16. A light ray reflects from a flat mirror. The incident ray is directed downward and to the right toward the mirror, and the reflected ray leaves upward and to the right. Which statement correctly describes the reflection?
    Answer: The normal bisects the angle between the incident and reflected rays. This question tests understanding of reflection. The law of reflection requires that the angle of incidence equals the angle of reflection, both measured from the normal. This means the normal line bisects the angle between the incident and reflected rays—it acts as the axis of symmetry for the reflection. The incident ray, normal, and reflected ray all lie in the same plane. Choice B incorrectly suggests the mirror surface bisects this angle, which would violate the law of reflection except when rays are perpendicular to the surface. Visualize reflection as a symmetric process about the normal, not about the surface.
17. A pulse on a taut string reaches a rigid wall. The incident pulse travels to the right toward the wall, and the reflected pulse travels to the left away from the wall. Which statement correctly describes the reflection at the rigid boundary?
    Answer: The reflected pulse is inverted relative to the incident pulse. This question tests understanding of reflection of mechanical waves at boundaries. When a wave pulse on a string encounters a rigid boundary (fixed end), the reflected pulse is inverted relative to the incident pulse because the boundary cannot move. The string must have zero displacement at the wall, so when the incident pulse tries to lift the string upward at the boundary, the reflected pulse must pull it downward to maintain this condition. Choice B incorrectly claims no inversion occurs, confusing wave speed (which doesn't change) with the boundary condition that determines pulse orientation. For mechanical wave reflections, remember that rigid boundaries invert pulses while free boundaries do not.
18. A transverse wave on a string reaches a boundary where the string is tied to a fixed support. The incident wave travels toward the support; the reflected wave travels away. Which statement correctly describes the reflection?
    Answer: The reflected wave has a $\pi$ phase shift relative to the incident wave This question tests understanding of reflection. When a transverse wave on a string reflects from a fixed boundary, the reflected wave undergoes a phase shift of π radians (180°), meaning the wave inverts. This occurs because the fixed support cannot move, creating a boundary condition where the displacement must be zero, which requires the incident and reflected waves to interfere destructively at the boundary. Choice B incorrectly claims no phase shift, misunderstanding that energy conservation doesn't prevent phase changes. Remember that fixed boundaries cause phase inversion (π shift) while free boundaries cause no phase shift.
19. A light ray in air strikes a flat mirror. The incident ray travels up and to the left and makes an angle $\theta_i$ with the normal. The reflected ray leaves traveling up and to the right. Which statement correctly describes the reflection?
    Answer: The reflected angle equals $\theta_i$ measured from the normal. This question tests understanding of reflection angles. The law of reflection states that the angle of incidence equals the angle of reflection, with both angles measured from the normal to the reflecting surface. Since the incident ray makes angle θᵢ with the normal, the reflected ray must also make angle θᵢ with the normal, traveling on the opposite side. Choice B incorrectly suggests the reflected angle is 90°-θᵢ, which would be the complementary angle—this error often arises from measuring angles relative to the surface instead of the normal. Always establish the normal at the point of incidence and measure both incident and reflected angles from this reference line.
20. A transverse wave on a string travels leftward toward a boundary where the string is tied to a light ring that can move freely up and down (an effectively free end). The incident wave is upward, and the reflected wave travels rightward. Which statement correctly describes the reflection?
    Answer: The reflected wave is not inverted relative to the incident wave. This question tests understanding of reflection. When a transverse wave on a string reflects from a free boundary (like a light ring that can move freely), the reflected wave is not inverted relative to the incident wave. At a free boundary, the string end can move without constraint, so an upward incident pulse creates an upward force that moves the ring up, generating an upward reflected pulse traveling back. This contrasts with rigid boundaries where inversion occurs. The wave maintains the same speed in the same medium but reverses direction. Choice B incorrectly claims all reflections invert waves, but inversion depends on boundary type: rigid boundaries invert, free boundaries don't. Remember the boundary condition determines reflection behavior: fixed ends invert pulses, free ends preserve orientation.

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