AP Physics 2: Algebra-Based Unit 5: Geometric Optics Practice Exam

Assessment for Unit 5: Geometric Optics

Estimated Time: 60 minutes

Exam Details

Questions: 32 total (32 multiple choice)
Time: 60 minutes (recommended)
Topics Covered: Unit 5: Geometric Optics
Format: Multiple Choice questions matching real exam difficulty
Scoring: Instant results with detailed explanations

A. Multiple-Choice Questions (32 Questions)

Select the one best answer for each question.

1. [Skill: 1.1 | Topic: 5.1] A monochromatic laser beam travels through the air and strikes a flat glass surface. Which of the following best describes the relationship between the light ray used to model the beam and the wavefronts of the light wave?

(A)The light ray is parallel to the wavefronts and points in the direction of energy propagation.(B)The light ray is perpendicular to the wavefronts and points in the direction of travel of the wave.(C)The light ray is oriented at a $45^\circ$ angle to the wavefronts to account for the transverse nature of light.(D)The light ray represents the crest of the wave, while the wavefronts represent the troughs.

2. [Skill: 1.4 | Topic: 5.1] A ray of light is incident on a stationary flat mirror. The angle between the incident ray and the reflected ray is measured to be $70^\circ$. What is the angle of incidence, $\theta_i$, and what is the angle between the incident ray and the surface of the mirror?

(A)$\theta_i = 70^\circ$; angle with surface = $20^\circ$(B)$\theta_i = 35^\circ$; angle with surface = $35^\circ$(C)$\theta_i = 35^\circ$; angle with surface = $55^\circ$(D)$\theta_i = 140^\circ$; angle with surface = $50^\circ$

3. [Skill: 1.1 | Topic: 5.1] A student observes two different surfaces: a highly polished silver tray and a sheet of white construction paper. When a single beam of light hits the silver tray, a sharp reflected beam is observed. When the same beam hits the paper, no sharp beam is seen, though the paper appears bright from all angles. Which of the following correctly characterizes these observations?

(A)The silver tray demonstrates diffuse reflection, while the paper demonstrates specular reflection.(B)The silver tray demonstrates specular reflection because its surface is smooth on a microscopic scale.(C)The paper violates the law of reflection because the reflected rays do not follow $\theta_i = \theta_r$.(D)The paper demonstrates specular reflection, but the light is absorbed before it can form a beam.

4. [Skill: 1.5 | Topic: 5.1] A ray of light is incident on a flat mirror at an angle of $20^\circ$ to the normal. If the mirror is rotated clockwise by $10^\circ$ about an axis through the point of incidence while the incident ray remains fixed, what is the new angle of reflection $\theta_r$ relative to the NEW normal, and what is the total angular displacement of the reflected ray from its original path?

(A)New $\theta_r = 30^\circ$; Displacement = $10^\circ$(B)New $\theta_r = 10^\circ$; Displacement = $20^\circ$(C)New $\theta_r = 30^\circ$; Displacement = $20^\circ$(D)New $\theta_r = 20^\circ$; Displacement = $10^\circ$

5. [Skill: 2.2 | Topic: 5.1] A student performs an experiment to test the law of reflection using a laser and a plane mirror. They record the angle of incidence $\theta_i$ and the angle of reflection $\theta_r$ for several trials but mistakenly measure the angles from the mirror surface rather than the normal. Which of the following best describes the result of their data analysis?

(A)The data will show that the angles are not equal, disproving the law of reflection.(B)The data will still show that the measured incident angle equals the measured reflected angle because of the geometric symmetry of the normal.(C)The measured angles will sum to $180^\circ$ in every trial.(D)The reflected angle will always be double the incident angle because of the shift in reference frame.

6. [Skill: 1.4 | Topic: 5.2] An object is placed at a distance $s_o = 2f$ from a concave mirror with focal length $f$. Which of the following best describes the characteristics of the image formed by the mirror?

(A)The image is real, inverted, and the same size as the object.(B)The image is real, upright, and larger than the object.(C)The image is virtual, upright, and larger than the object.(D)The image is real, inverted, and smaller than the object.

7. [Skill: 2.2 | Topic: 5.2] A small light bulb is placed $20$ cm in front of a convex security mirror that has a focal length of magnitude $10$ cm. What is the location and type of the image formed?

(A)6.7 cm in front of the mirror; real image(B)6.7 cm behind the mirror; virtual image(C)20 cm behind the mirror; virtual image(D)10 cm in front of the mirror; real image

8. [Skill: 1.1 | Topic: 5.2] Which of the following statements correctly explains the physical difference between a real image and a virtual image formed by a curved mirror?

(A)A real image can only be formed by a convex mirror, while a virtual image can only be formed by a concave mirror.(B)A real image is formed by the actual intersection of reflected light rays, whereas a virtual image is formed where diverging reflected rays appear to originate.(C)A real image is always upright, while a virtual image is always inverted.(D)A real image is formed behind the mirror surface, while a virtual image is formed in front of the mirror surface.

9. [Skill: 2.2 | Topic: 5.2] An object is placed at a distance $s_o = 0.5f$ in front of a concave mirror of focal length $f$. What is the magnification $M$ of the resulting image?

(A)M = -2(B)M = +0.5(C)M = +2(D)M = -0.5

10. [Skill: 5.1 | Topic: 5.2] An object is initially placed very far from a concave mirror ($s_o \gg f$) and is slowly moved toward the focal point $f$. Which of the following correctly describes the motion and change in size of the image during this process?

(A)The image moves closer to the mirror and decreases in size.(B)The image moves away from the mirror and increases in size.(C)The image moves away from the mirror and decreases in size.(D)The image moves closer to the mirror and increases in size.

11. [Skill: 2.2 | Topic: 5.3] A light ray travels from water (index of refraction $n_w = 1.33$) into a diamond (index of refraction $n_d = 2.42$). Which of the following expressions correctly represents the ratio of the speed of light in water to the speed of light in diamond ($v_w / v_d$)?

(A)$\frac{1.33}{2.42}$(B)$\frac{2.42}{1.33}$(C)$1.33 \times 2.42$(D)$\frac{1}{1.33 \times 2.42}$

12. [Skill: 1.1 | Topic: 5.3] A beam of monochromatic light passes from Medium 1 into Medium 2. An observer notes that the light ray bends away from the normal as it enters Medium 2. Which of the following correctly compares the speed of light ($v$) and the index of refraction ($n$) in the two media?

(A)$v_2 > v_1$ and $n_2 < n_1$(B)$v_2 < v_1$ and $n_2 > n_1$(C)$v_2 > v_1$ and $n_2 > n_1$(D)$v_2 < v_1$ and $n_2 < n_1$

13. [Skill: 1.1 | Topic: 5.4] A student is performing an experiment with a thin diverging (concave) lens. They direct several light rays parallel to the principal axis toward the lens. Which of the following best describes the behavior of the rays after they pass through the lens? (A) The rays converge at a single point located at the focal distance $f$ on the side of the lens opposite the light source. (B) The rays diverge from each other such that they appear to originate from a single point located at the focal distance $f$ on the same side of the lens as the light source. (C) The rays pass through the lens without changing direction because the lens is thin. (D) The rays reflect off the front surface of the lens and converge at a point halfway between the source and the lens.

(A)The rays converge at a single point located at the focal distance $f$ on the side of the lens opposite the light source.(B)The rays diverge from each other such that they appear to originate from a single point located at the focal distance $f$ on the same side of the lens as the light source.(C)The rays pass through the lens without changing direction because the lens is thin.(D)The rays reflect off the front surface of the lens and converge at a point halfway between the source and the lens.

14. [Skill: 2.2 | Topic: 5.4] An object is placed 30 cm in front of a thin convex (converging) lens with a focal length of 10 cm. Which of the following correctly identifies the image distance $s_i$ and the magnification $M$ of the resulting image? (A) $s_i = 15 \text{ cm}$ and $M = -0.5$ (B) $s_i = 15 \text{ cm}$ and $M = -2.0$ (C) $s_i = 7.5 \text{ cm}$ and $M = -0.25$ (D) $s_i = -15 \text{ cm}$ and $M = +0.5$

(A)$s_i = 15 \text{ cm}$ and $M = -0.5$(B)$s_i = 15 \text{ cm}$ and $M = -2.0$(C)$s_i = 7.5 \text{ cm}$ and $M = -0.25$(D)$s_i = -15 \text{ cm}$ and $M = +0.5$

15. [Skill: 1.4 | Topic: 5.4] A light bulb is placed at the focal point of a thin converging lens. A screen is placed on the opposite side of the lens at a distance of $2f$. Which of the following best describes what will be observed on the screen? (A) A sharp, upright image of the light bulb filament that is twice the size of the original. (B) A sharp, inverted image of the light bulb filament that is the same size as the original. (C) A blurry circle of light because the rays emerging from the lens are parallel to the principal axis. (D) No light at all, because all light rays are reflected back toward the bulb at the focal point.

(A)A sharp, upright image of the light bulb filament that is twice the size of the original.(B)A sharp, inverted image of the light bulb filament that is the same size as the original.(C)A blurry circle of light because the rays emerging from the lens are parallel to the principal axis.(D)No light at all, because all light rays are reflected back toward the bulb at the focal point.

16. [Skill: 1.1 | Topic: 5.1] A series of parallel wavefronts representing a monochromatic light wave is traveling through the air. Which of the following best describes the relationship between these wavefronts and the light rays used to model the beam's path in geometric optics?

(A)The light rays are parallel to the wavefronts and point in the direction of wave propagation.(B)The light rays are perpendicular to the wavefronts and point in the direction of wave propagation.(C)The light rays are perpendicular to the wavefronts and point opposite to the direction of wave propagation.(D)The light rays oscillate sinusoidally around the wavefronts to represent the electric field.

Refer to the figure below.

17. [Skill: 2.2 | Topic: 5.1] A ray of light is incident upon a flat, polished silver mirror. The angle between the incident ray and the surface of the mirror is $35^{\circ}$. What is the angle of reflection, $\theta_r$, measured from the normal to the surface?

(A)$35^{\circ}$(B)$55^{\circ}$(C)$70^{\circ}$(D)$145^{\circ}$

18. [Skill: 1.4 | Topic: 5.1] A beam of parallel light rays strikes a rough, unpolished piece of white paper. Which of the following best explains why the light is reflected in many different directions (diffuse reflection) rather than in a single direction (specular reflection)?

(A)The law of reflection does not apply to light striking non-metallic or rough surfaces.(B)The incident rays strike the surface at different angles of incidence because the local normal at each point of contact varies in direction.(C)The rough surface absorbs the light rays and re-emits them as new wavefronts in random directions.(D)The light rays are refracted by the microscopic fibers of the paper before being reflected by the back surface.

Refer to the figure below.

19. [Skill: 2.2 | Topic: 5.1] Two plane mirrors are positioned perpendicular to each other (at a $90^{\circ}$ angle). A light ray enters the system and strikes Mirror 1 at an angle of $30^{\circ}$ relative to the normal of Mirror 1. The ray then reflects and strikes Mirror 2. What is the angle of reflection from Mirror 2, measured relative to the normal of Mirror 2?

(A)$30^{\circ}$(B)$45^{\circ}$(C)$60^{\circ}$(D)$90^{\circ}$

20. [Skill: 6.4 | Topic: 5.1] A student points a laser at a smooth glass window. The student observes a bright spot on a nearby wall where the reflected beam hits, but cannot see the path of the beam through the air between the laser and the window. Which of the following changes would most likely allow the student to see the path of the light ray through the air?

(A)Replacing the glass window with a highly polished silver mirror to increase specular reflection.(B)Using a higher-powered laser to increase the intensity of the light wavefronts.(C)Filling the air in the room with smoke or dust particles to encourage diffuse reflection of the beam's light.(D)Turning off all the lights in the room to make the laser beam appear brighter relative to the background.

21. [Skill: 1.1 | Topic: 5.2] An object is placed at a distance of $2f$ from a concave mirror, where $f$ is the focal length of the mirror. Which of the following best describes the characteristics of the image formed and the behavior of the reflected light rays?

(A)The reflected rays converge at a point $2f$ in front of the mirror, forming a real, inverted image of the same size as the object.(B)The reflected rays converge at a point $f$ in front of the mirror, forming a real, upright image that is smaller than the object.(C)The reflected rays diverge from the mirror and appear to originate from a point $2f$ behind the mirror, forming a virtual, upright image.(D)The reflected rays are parallel to each other, and no image is formed at any finite distance from the mirror.

22. [Skill: 2.2 | Topic: 5.2] A candle is placed 15 cm in front of a concave mirror that has a radius of curvature of 20 cm. What is the location and magnification of the image formed by the mirror?

(A)The image is located 30 cm in front of the mirror with a magnification of -2.0.(B)The image is located 30 cm behind the mirror with a magnification of +2.0.(C)The image is located 6.0 cm in front of the mirror with a magnification of -0.4.(D)The image is located 10 cm behind the mirror with a magnification of +0.67.

23. [Skill: 1.4 | Topic: 5.2] A student observes an image in a mirror that is upright and exactly one-half the size of the object. Which of the following conclusions must be true about the mirror and the image?

(A)The mirror is concave, and the image is real.(B)The mirror is concave, and the image is virtual.(C)The mirror is convex, and the image is real.(D)The mirror is convex, and the image is virtual.

Refer to the figure below.

24. [Skill: 1.1 | Topic: 5.2] An object is placed at a distance $s_o$ from a convex mirror with a focal length of magnitude $L$. Which of the following ray diagrams correctly represents the formation of the image, and what are the properties of that image?

(A)[Image Cue]: Rays from the object's top hit the mirror and converge at a point $L$ behind the mirror; the image is real and inverted.(B)[Image Cue]: A ray parallel to the principal axis reflects such that its extension passes through the focal point behind the mirror; the image is virtual and upright.(C)[Image Cue]: A ray directed toward the focal point behind the mirror reflects back through the object's position; the image is real and upright.(D)[Image Cue]: All reflected rays intersect at a point $s_i > s_o$ in front of the mirror; the image is virtual and enlarged.

25. [Skill: 6.4 | Topic: 5.2] A student is performing an experiment with a concave mirror of focal length $f$. The student places a screen at various distances in front of the mirror to capture an image. If the object is moved from a position $s_o = 3f$ to a position $s_o = 1.5f$, how does the required screen position and the size of the captured image change?

(A)The screen must be moved closer to the mirror, and the image size decreases.(B)The screen must be moved closer to the mirror, and the image size increases.(C)The screen must be moved farther from the mirror, and the image size decreases.(D)The screen must be moved farther from the mirror, and the image size increases.

26. [Skill: 1.4 | Topic: 5.3] Questions 1 and 2 refer to the following stimulus: A monochromatic light ray travels through air ($n_{air} = 1.0$) and strikes the surface of a flat glass block ($n_{glass} = 1.5$) at an angle of incidence $\theta_1 = 30^\circ$ relative to the normal. Which of the following correctly describes the change in the light ray's properties as it enters the glass block?

(A)The speed of the light ray increases, and the ray bends away from the normal.(B)The speed of the light ray increases, and the ray bends toward the normal.(C)The speed of the light ray decreases, and the ray bends away from the normal.(D)The speed of the light ray decreases, and the ray bends toward the normal.

Refer to the figure below.

27. [Skill: 6.4 | Topic: 5.3] An optical fiber consists of a core with an index of refraction $n_{core} = 1.50$ surrounded by a cladding with an index of refraction $n_{cladding} = 1.40$. Which of the following conditions is required for a light ray to undergo total internal reflection at the core-cladding interface?

(A)The light ray must be traveling in the cladding and strike the interface at an angle less than $68.9^\circ$ relative to the normal.(B)The light ray must be traveling in the core and strike the interface at an angle greater than $68.9^\circ$ relative to the normal.(C)The light ray must be traveling in the cladding and strike the interface at an angle greater than $21.1^\circ$ relative to the normal.(D)The light ray must be traveling in the core and strike the interface at an angle less than $21.1^\circ$ relative to the normal.

Refer to the figure below.

28. [Skill: 5.1 | Topic: 5.3] In a laboratory experiment, students measure the angle of incidence $\theta_i$ in air and the angle of refraction $\theta_r$ in an unknown liquid. They plot $\sin\theta_i$ on the vertical axis and $\sin\theta_r$ on the horizontal axis. The resulting graph is a straight line passing through the origin with a slope of 1.33. What physical quantity does the slope of this graph represent, and what is the speed of light in the liquid?

(A)The slope represents the index of refraction of the liquid; the speed is approximately $2.26 \times 10^8$ m/s.(B)The slope represents the index of refraction of the liquid; the speed is approximately $3.99 \times 10^8$ m/s.(C)The slope represents the reciprocal of the index of refraction; the speed is approximately $2.26 \times 10^8$ m/s.(D)The slope represents the reciprocal of the index of refraction; the speed is approximately $3.99 \times 10^8$ m/s.

29. [Skill: 1.1 | Topic: 5.4] A student places an object in front of a thin diverging (concave) lens. The object is located at a distance from the lens equal to twice the focal length ($s_o = 2|f|$). Which of the following correctly describes the image formed by the lens?

(A)Real, inverted, and smaller than the object.(B)Real, upright, and larger than the object.(C)Virtual, upright, and smaller than the object.(D)Virtual, inverted, and larger than the object.

Refer to the figure below.

30. [Skill: 2.2 | Topic: 5.4] An experiment is conducted with a thin converging lens to determine its focal length. A student measures the object distance $s_o$ and the resulting image distance $s_i$ for several trials and creates a graph of $\frac{1}{s_i}$ as a function of $\frac{1}{s_o}$. [Image Cue]: Graph, Linear plot of 1/s_i vs 1/s_o, The vertical intercept is 0.10 cm$^{-1}$ and the horizontal intercept is 0.10 cm$^{-1}$ with a slope of -1. Based on the graph, what is the focal length $f$ of the lens?

(A)0.10 cm(B)5.0 cm(C)10 cm(D)20 cm

31. [Skill: 1.4 | Topic: 5.4] A lightbulb is placed at a distance of $30$ cm from a thin converging lens with a focal length of $10$ cm. The lightbulb is then moved to a new position $15$ cm from the lens. Which of the following describes the change in the image's characteristics as the lightbulb moves from $30$ cm to $15$ cm?

(A)The image remains real and becomes smaller.(B)The image remains real and becomes larger.(C)The image changes from real to virtual and becomes smaller.(D)The image changes from virtual to real and becomes larger.

32. [Skill: 6.4 | Topic: 5.4] A student uses a thin converging lens to project a sharp image of a distant tree onto a screen. The tree is so far away that the light rays incident on the lens are effectively parallel to the principal axis. If the student replaces the lens with a different thin converging lens that has a greater curvature (is thicker in the middle), how must the screen be moved to capture a sharp image, and why?

(A)The screen must be moved closer to the lens because a lens with greater curvature has a shorter focal length.(B)The screen must be moved further from the lens because a lens with greater curvature has a longer focal length.(C)The screen must be moved closer to the lens because the parallel rays will now diverge more before converging.(D)The screen does not need to be moved because the incident rays are parallel.

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