#Mirrors: Your Ultimate AP Physics 2 Guide

Hey there, future physicist! Let's dive into the world of mirrors. This guide is designed to be your go-to resource, especially the night before the exam. We'll break down everything you need to know about image formation by mirrors, making it super clear and easy to remember. Let's ace this!

Mirrors are a high-value topic in AP Physics 2, frequently appearing in both multiple-choice and free-response questions. Understanding the concepts thoroughly will boost your confidence and score.

# Image Formation by Mirrors

Mirrors form images through reflection. The type of mirror affects how light rays converge or diverge, influencing the image's characteristics. Let's break it down:

#Focal Points

# Concave Mirrors (Converging)

Definition: Concave mirrors curve inward, like a cave. They're also known as converging mirrors.
Focal Point: Incident light rays parallel to the principal axis converge at a real focal point in front of the mirror. 🔍
Image Formation: Concave mirrors can form both real and virtual images, depending on the object's distance.

Key Concept

Concave mirrors can produce both real and virtual images, which is a key concept for AP Physics 2. Remember that real images can be projected onto a screen, while virtual images cannot.

# Convex Mirrors (Diverging)

Definition: Convex mirrors bulge outward, like the back of a spoon. They're also known as diverging mirrors.
Focal Point: Incident light rays parallel to the principal axis diverge, appearing to originate from a virtual focal point behind the mirror.
Image Formation: Convex mirrors always form virtual, upright, and reduced images.

Quick Fact

Convex mirrors always produce virtual, upright, and smaller images. This is a quick fact to remember for multiple-choice questions.

# Plane Mirrors

Definition: Plane mirrors are flat mirrors.
Focal Point: The focal point is at infinity. Incident light rays reflect without converging or diverging.
Image Formation: Plane mirrors form virtual, upright, and same-size images. The image appears to be the same distance behind the mirror as the object is in front of it.

Memory Aid

Plane mirrors: Think of a mirror in your bathroom. It shows you an image that is the same size and distance away from the mirror as you are, but it's flipped left to right.

# Spherical Mirrors

Focal Point Approximation: For small apertures, the focal point is approximately halfway between the mirror's surface and the center of curvature.
Focal Length ( $f$ ): The distance from the mirror's surface to its focal point.

Exam Tip

Remember, the focal length ( $f$ ) is half the radius of curvature ( $R$ ). This is a common relationship used in calculations: $f = \frac{R}{2}$

#Real vs. Virtual Images

Real Images: Formed when light rays converge in front of the mirror. They can be projected onto a screen. 📷
Virtual Images: Formed when light rays appear to diverge from behind the mirror. They cannot be projected onto a screen.

Common Mistake

Students often confuse real and virtual images. Remember, real images are formed by actual convergence of light rays and can be projected, while virtual images are formed by apparent divergence and cannot.

#Image Location and Focal Length

Image Location: Depends on the mirror's focal length and the object's distance from the mirror.
Sign Conventions: Distances to the left of the mirror (real side) are positive, and distances to the right (virtual side) are negative.
Plane Mirror: The image distance equals the object distance. If an object is 30 cm in front of a plane mirror, its virtual image will appear 30 cm behind the mirror.

#Image Magnification ( $M$ )

Definition: The ratio of the image size to the object size.
Formula: $|M|=\left|\frac{h_{i}}{h_{o}}\right|=\left|\frac{s_{i}}{s_{o}}\right|$ , where $h_i$ and $h_o$ are the image and object heights, and $s_i$ and $s_o$ are the image and object distances from the mirror.
Magnification > 1: Enlarged image.
Magnification < 1: Reduced image.
Sign of Magnification: Positive for upright images, negative for inverted images.

Memory Aid

Remember the magnification formula using the acronym "HISO": Height Image / Height Object = Size Image / Size Object

#Ray Diagrams for Mirrors

Purpose: To determine the location, type, size, and orientation of images. 🎨
Principal Rays:
1. Parallel Ray: A ray parallel to the principal axis reflects through the focal point (concave) or appears to come from the focal point (convex).
2. Center Ray: A ray that strikes the center of the mirror reflects at the same angle.
3. Focal Ray: A ray passing through the focal point (concave) or directed toward the focal point (convex) reflects parallel to the principal axis.
Image Characteristics: Images can be upright or inverted, virtual or real, and reduced, enlarged, or the same size as the object.
Concave Mirrors: Can form both real and virtual images.
Convex Mirrors: Only form virtual images.

Exam Tip

When drawing ray diagrams, always use a ruler and draw the principal rays accurately. The intersection of at least two reflected rays will give you the image location. Also, always draw the object first.

Practice Question

Multiple Choice Questions

A concave mirror has a focal length of 20 cm. An object is placed 30 cm in front of the mirror. Which of the following best describes the image formed? (A) Real, inverted, and smaller (B) Real, inverted, and larger (C) Virtual, upright, and smaller (D) Virtual, upright, and larger
A convex mirror always produces an image that is: (A) Real and inverted (B) Real and upright (C) Virtual and inverted (D) Virtual and upright
An object is placed 15 cm in front of a plane mirror. What is the distance between the object and its image? (A) 7.5 cm (B) 15 cm (C) 30 cm (D) 0 cm

Free Response Question

An object of height 2 cm is placed 30 cm in front of a concave mirror with a focal length of 20 cm.

(a) Draw a ray diagram to show the formation of the image. Clearly label the object, image, focal point, and mirror.

(b) Calculate the image distance using the mirror equation: $\frac{1}{f} = \frac{1}{s_o} + \frac{1}{s_i}$

(d) Determine the height of the image.

(e) State whether the image is real or virtual and upright or inverted.

Answer Key and Scoring Rubric

Multiple Choice Answers:

Free Response Question:

(a) Ray Diagram (4 points) - 1 point for correctly drawing the mirror and principal axis. - 1 point for correctly drawing the object. - 1 point for drawing at least two principal rays accurately. - 1 point for correctly locating the image.

(b) Image Distance (3 points) - 1 point for using the mirror equation correctly: $\frac{1}{20} = \frac{1}{30} + \frac{1}{s_i}$ - 1 point for correct substitution. - 1 point for correct answer: $s_i = 60$ cm

(c) Magnification (2 points) - 1 point for using the magnification formula: $M = -\frac{s_i}{s_o}$ - 1 point for correct answer: $M = -2$

(d) Image Height (2 points) - 1 point for using the magnification formula: $M = \frac{h_i}{h_o}$ - 1 point for correct answer: $h_i = -4$ cm

(e) Image Characteristics (2 points) - 1 point for stating the image is real. - 1 point for stating the image is inverted.

#Final Exam Focus

Alright, you're in the home stretch! Here’s what to focus on for the exam:

High Priority Topics: Image formation by concave, convex, and plane mirrors, ray diagrams, and magnification.
Common Question Types: Multiple-choice questions testing your understanding of image characteristics and calculations involving the mirror equation and magnification. Free-response questions often involve drawing ray diagrams and calculating image properties.
Time Management: Practice drawing ray diagrams quickly and accurately. Memorize the sign conventions and magnification formula.
Common Pitfalls: Confusing real and virtual images, incorrect sign conventions, and inaccurate ray diagrams. Double-check your work.

Exam Tip

Remember that AP Physics 2 often combines multiple concepts. Be prepared to apply your knowledge of mirrors in conjunction with other topics like optics and wave phenomena.

Keep calm, stay focused, and you've got this! You're well-prepared to rock the AP Physics 2 exam. Good luck!

#Mirrors: Your Ultimate AP Physics 2 Guide

# Image Formation by Mirrors

Mirrors form images through reflection. The type of mirror affects how light rays converge or diverge, influencing the image's characteristics. Let's break it down:

#Focal Points

# Concave Mirrors (Converging)

Definition: Concave mirrors curve inward, like a cave. They're also known as converging mirrors.
Focal Point: Incident light rays parallel to the principal axis converge at a real focal point in front of the mirror. 🔍
Image Formation: Concave mirrors can form both real and virtual images, depending on the object's distance.

Key Concept

Concave mirrors can produce both real and virtual images, which is a key concept for AP Physics 2. Remember that real images can be projected onto a screen, while virtual images cannot.

# Convex Mirrors (Diverging)

Definition: Convex mirrors bulge outward, like the back of a spoon. They're also known as diverging mirrors.
Focal Point: Incident light rays parallel to the principal axis diverge, appearing to originate from a virtual focal point behind the mirror.
Image Formation: Convex mirrors always form virtual, upright, and reduced images.

Quick Fact

Convex mirrors always produce virtual, upright, and smaller images. This is a quick fact to remember for multiple-choice questions.

# Plane Mirrors

Definition: Plane mirrors are flat mirrors.
Focal Point: The focal point is at infinity. Incident light rays reflect without converging or diverging.
Image Formation: Plane mirrors form virtual, upright, and same-size images. The image appears to be the same distance behind the mirror as the object is in front of it.

Memory Aid

Plane mirrors: Think of a mirror in your bathroom. It shows you an image that is the same size and distance away from the mirror as you are, but it's flipped left to right.

# Spherical Mirrors

Focal Point Approximation: For small apertures, the focal point is approximately halfway between the mirror's surface and the center of curvature.
Focal Length ( $f$ ): The distance from the mirror's surface to its focal point.

Exam Tip

Remember, the focal length ( $f$ ) is half the radius of curvature ( $R$ ). This is a common relationship used in calculations: $f = \frac{R}{2}$

#Real vs. Virtual Images

Real Images: Formed when light rays converge in front of the mirror. They can be projected onto a screen. 📷
Virtual Images: Formed when light rays appear to diverge from behind the mirror. They cannot be projected onto a screen.

Common Mistake

#Image Location and Focal Length

Image Location: Depends on the mirror's focal length and the object's distance from the mirror.
Sign Conventions: Distances to the left of the mirror (real side) are positive, and distances to the right (virtual side) are negative.
Plane Mirror: The image distance equals the object distance. If an object is 30 cm in front of a plane mirror, its virtual image will appear 30 cm behind the mirror.

#Image Magnification ( $M$ )

Definition: The ratio of the image size to the object size.
Formula: $|M|=\left|\frac{h_{i}}{h_{o}}\right|=\left|\frac{s_{i}}{s_{o}}\right|$ , where $h_i$ and $h_o$ are the image and object heights, and $s_i$ and $s_o$ are the image and object distances from the mirror.
Magnification > 1: Enlarged image.
Magnification < 1: Reduced image.
Sign of Magnification: Positive for upright images, negative for inverted images.

Memory Aid

Remember the magnification formula using the acronym "HISO": Height Image / Height Object = Size Image / Size Object

#Ray Diagrams for Mirrors

Purpose: To determine the location, type, size, and orientation of images. 🎨
Principal Rays:
1. Parallel Ray: A ray parallel to the principal axis reflects through the focal point (concave) or appears to come from the focal point (convex).
2. Center Ray: A ray that strikes the center of the mirror reflects at the same angle.
3. Focal Ray: A ray passing through the focal point (concave) or directed toward the focal point (convex) reflects parallel to the principal axis.
Image Characteristics: Images can be upright or inverted, virtual or real, and reduced, enlarged, or the same size as the object.
Concave Mirrors: Can form both real and virtual images.
Convex Mirrors: Only form virtual images.

Exam Tip

Practice Question

Multiple Choice Questions

A concave mirror has a focal length of 20 cm. An object is placed 30 cm in front of the mirror. Which of the following best describes the image formed? (A) Real, inverted, and smaller (B) Real, inverted, and larger (C) Virtual, upright, and smaller (D) Virtual, upright, and larger
A convex mirror always produces an image that is: (A) Real and inverted (B) Real and upright (C) Virtual and inverted (D) Virtual and upright
An object is placed 15 cm in front of a plane mirror. What is the distance between the object and its image? (A) 7.5 cm (B) 15 cm (C) 30 cm (D) 0 cm

Free Response Question

An object of height 2 cm is placed 30 cm in front of a concave mirror with a focal length of 20 cm.

(a) Draw a ray diagram to show the formation of the image. Clearly label the object, image, focal point, and mirror.

(b) Calculate the image distance using the mirror equation: $\frac{1}{f} = \frac{1}{s_o} + \frac{1}{s_i}$

(d) Determine the height of the image.

(e) State whether the image is real or virtual and upright or inverted.

Answer Key and Scoring Rubric

Multiple Choice Answers:

Free Response Question:

(c) Magnification (2 points) - 1 point for using the magnification formula: $M = -\frac{s_i}{s_o}$ - 1 point for correct answer: $M = -2$

(d) Image Height (2 points) - 1 point for using the magnification formula: $M = \frac{h_i}{h_o}$ - 1 point for correct answer: $h_i = -4$ cm

(e) Image Characteristics (2 points) - 1 point for stating the image is real. - 1 point for stating the image is inverted.

#Final Exam Focus

Alright, you're in the home stretch! Here’s what to focus on for the exam:

High Priority Topics: Image formation by concave, convex, and plane mirrors, ray diagrams, and magnification.
Common Question Types: Multiple-choice questions testing your understanding of image characteristics and calculations involving the mirror equation and magnification. Free-response questions often involve drawing ray diagrams and calculating image properties.
Time Management: Practice drawing ray diagrams quickly and accurately. Memorize the sign conventions and magnification formula.
Common Pitfalls: Confusing real and virtual images, incorrect sign conventions, and inaccurate ray diagrams. Double-check your work.

Exam Tip

Remember that AP Physics 2 often combines multiple concepts. Be prepared to apply your knowledge of mirrors in conjunction with other topics like optics and wave phenomena.

Keep calm, stay focused, and you've got this! You're well-prepared to rock the AP Physics 2 exam. Good luck!

Images Formed by Mirrors

Jackson Hernandez

#Mirrors: Your Ultimate AP Physics 2 Guide

# Image Formation by Mirrors

#Focal Points

# Concave Mirrors (Converging)

# Convex Mirrors (Diverging)

# Plane Mirrors

# Spherical Mirrors

#Real vs. Virtual Images

#Image Location and Focal Length

#Image Magnification ( $M$ )

#Ray Diagrams for Mirrors

#Final Exam Focus

Explore more resources

How are we doing?

Images Formed by Mirrors

Jackson Hernandez

#Mirrors: Your Ultimate AP Physics 2 Guide

# Image Formation by Mirrors

#Focal Points

# Concave Mirrors (Converging)

# Convex Mirrors (Diverging)

# Plane Mirrors

# Spherical Mirrors

#Real vs. Virtual Images

#Image Location and Focal Length

#Image Magnification ( $M$ )

#Ray Diagrams for Mirrors

#Final Exam Focus

Explore more resources

How are we doing?

Images Formed by Mirrors

Jackson Hernandez

#Mirrors: Your Ultimate AP Physics 2 Guide

# Image Formation by Mirrors

#Focal Points

# Concave Mirrors (Converging)

# Convex Mirrors (Diverging)

# Plane Mirrors

# Spherical Mirrors

#Real vs. Virtual Images

#Image Location and Focal Length

#Image Magnification (MMM)

#Ray Diagrams for Mirrors

#Final Exam Focus

Explore more resources

How are we doing?

Images Formed by Mirrors

Jackson Hernandez

#Mirrors: Your Ultimate AP Physics 2 Guide

# Image Formation by Mirrors

#Focal Points

# Concave Mirrors (Converging)

# Convex Mirrors (Diverging)

# Plane Mirrors

# Spherical Mirrors

#Real vs. Virtual Images

#Image Location and Focal Length

#Image Magnification (MMM)

#Ray Diagrams for Mirrors

#Final Exam Focus

Explore more resources

How are we doing?

#Image Magnification ( $M$ )

#Image Magnification ( $M$ )