Chapter 23

Standing \(2.5 \mathrm{~m}\) in front of a plane mirror with your camera, you decide to take a picture of yourself. To what distance should the camera be focused to get a sharp image?

A man stands \(2.0 \mathrm{~m}\) away from a plane mirror. (a) What is the distance between the mirror and the man's image? (b) What are the image characteristics?

An object \(5.0 \mathrm{~cm}\) tall is placed \(40 \mathrm{~cm}\) from a plane mirror. Find (a) the distance from the object to the image, (b) the height of the image, and (c) the image's magnification.

If you hold a \(900-\mathrm{cm}^{2}\) square plane mirror \(45 \mathrm{~cm}\) from your eyes and can just see the full length of an 8.5-m flagpole behind you, how far are you from the pole? [Hint: A diagram is helpful.]

A small dog sits \(3.0 \mathrm{~m}\) in front of a plane mirror. (a) Where is the dog's image in relation to the mirror? (b) If the dog jumps at the mirror at a speed of \(1.0 \mathrm{~m} / \mathrm{s}\), how fast does the dog approach its image?

A woman fixing the hair on the back of her head holds a plane mirror \(30 \mathrm{~cm}\) in front of her face so as to look into a plane mirror on the bathroom wall behind her. She is \(90 \mathrm{~cm}\) from the wall mirror. (a) The image of the back of her head will be from (1) only the front mirror, (2) only the wall mirror, or (3) both mirrors. (b) Approximately how far does the image of the back of her head appear in front of her?

(a) When you stand between two plane mirrors on opposite walls in a dance studio, you observe (1) one, (2) two, or (3) multiple images. Explain. (b) If you stand \(3.0 \mathrm{~m}\) from the mirror on the north wall and \(5.0 \mathrm{~m}\) from the mirror on the south wall, what are the image distances for the first two images in both mirrors?

A woman \(1.7 \mathrm{~m}\) tall stands \(3.0 \mathrm{~m}\) in front of a plane mirror. (a) What is the minimum height the mirror must be to allow the woman to view her complete image from head to foot? Assume that her eyes are \(10 \mathrm{~cm}\) below the top of her head. (b) What would be the required minimum height of the mirror if she were to stand \(5.0 \mathrm{~m}\) away?

An object is \(100 \mathrm{~cm}\) in front of a concave mirror that has a radius of \(80 \mathrm{~cm} .\) (a) Use a ray diagram to determine whether the image is (1) real or virtual, (2) upright or inverted, and (3) magnified or reduced. (b) Calculate the image distance and lateral magnification.

A candle with a flame \(1.5 \mathrm{~cm}\) tall is placed \(5.0 \mathrm{~cm}\) from the front of a concave mirror. A virtual image is formed \(10 \mathrm{~cm}\) behind the mirror. (a) Find the focal length and radius of curvature of the mirror. (b) How tall is the image of the flame?

An object is placed \(50 \mathrm{~cm}\) in front of a convex mirror and its image is found to be \(20 \mathrm{~cm}\) behind the mirror. What is the focal length of the mirror? What is the lateral magnification?

An object \(3.0 \mathrm{~cm}\) tall is placed \(20 \mathrm{~cm}\) from the front of a concave mirror with a radius of curvature of \(30 \mathrm{~cm}\). Where is the image formed, and how tall is it?

An object \(3.0 \mathrm{~cm}\) tall is placed at different locations in front of a concave mirror whose radius of curvature is \(30 \mathrm{~cm} .\) Determine the location of the image and its characteristics when the object distance is \(40 \mathrm{~cm}, 30 \mathrm{~cm}\) \(15 \mathrm{~cm},\) and \(5.0 \mathrm{~cm},\) using (a) a ray diagram and (b) the mirror equation.

Use the mirror equation and the magnification factor to show that when \(d_{\mathrm{o}}=R=2 f\) for a concave mirror, the image is real, inverted, and the same size as the object.

An object is \(120 \mathrm{~cm}\) in front of a convex mirror that has a focal length of \(50 \mathrm{~cm}\). (a) Use a ray diagram to determine whether the image is (1) real or virtual, (2) upright or inverted, and (3) magnified or reduced. (b) Calculate the image distance and image height.

A bottle \(6.0 \mathrm{~cm}\) tall is located \(75 \mathrm{~cm}\) from the concave surface of a mirror with a radius of curvature of \(50 \mathrm{~cm}\). Where is the image located, and what are its characteristics?

A virtual image of magnification +2.0 is produced when an object is placed \(7.0 \mathrm{~cm}\) in front of a spherical mirror. (a) The mirror is (1) convex, (2) concave, (3) flat. Explain. (b) Find the radius of curvature of the mirror.

A virtual image of magnification +0.50 is produced when an object is placed \(5.0 \mathrm{~cm}\) in front of a spherical mirror. (a) The mirror is (1) convex, (2) concave, (3) flat. Explain. (b) Find the radius of curvature of the mirror.

Using the spherical mirror equation and the magnification factor, show that for a convex mirror, the image of an object is always virtual, upright, and reduced.

When a man's face is in front of a concave mirror of radius \(100 \mathrm{~cm}\), the lateral magnification of the image is \(+1.5 .\) What is the image distance?

A convex mirror in a department store produces an upright image 0.25 times the size of a person who is standing \(200 \mathrm{~cm}\) from the mirror. What is the focal length of the mirror?

The image of an object located \(30 \mathrm{~cm}\) from a mirror is formed on a screen located \(20 \mathrm{~cm}\) from the mirror. (a) The mirror is (1) convex, (2) concave, (3) flat. Explain. (b) What is the mirror's radius of curvature?

The upright image of an object \(18 \mathrm{~cm}\) in front of a mirror is half the size of the object. (a) The mirror is (1) convex, (2) concave, (3) flat. Explain. (b) What is the focal length of the mirror?

A concave mirror is constructed so that a man at a distance of \(20 \mathrm{~cm}\) from the mirror sees his image magnified 2.5 times. What is the radius of curvature of the mirror?

A child looks at a reflective Christmas tree ball ornament that has a diameter of \(9.0 \mathrm{~cm}\) and sees an image of her face that is half the real size. How far is the child's face from the ball?

A dentist uses a spherical mirror that produces an upright image of a tooth that is magnified four times. (a) The mirror is (1) converging, (2) diverging, (3) flat. Explain. (b) What is the mirror's focal length in terms of the object distance?

A 15-cm-long pencil is placed with its eraser on the optic axis of a concave mirror and its point directed upward at a distance of \(20 \mathrm{~cm}\) in front of the mirror. The radius of curvature of the mirror is \(30 \mathrm{~cm}\). Use (a) a ray diagram and (b) the mirror equation to locate the image and determine the image characteristics.

A spherical mirror at an amusement park has a radius of \(10 \mathrm{~m}\). If it forms an image that has a lateral magnification of \(+2.0,\) what are the object and image distances?

A pill bottle \(3.0 \mathrm{~cm}\) tall is placed \(12 \mathrm{~cm}\) in front of a mirror. A 9.0-cm-tall upright image is formed. (a) The mirror is (1) convex, (2) concave, (3) flat. Explain. (b) What is its radius of curvature?

A convex mirror is on the exterior of the passenger side of many trucks (see Conceptional Question \(8 \mathrm{a}\) ). If the focal length of such a mirror is \(-40.0 \mathrm{~cm}\), what will be the location and height of the image of a car that is \(2.0 \mathrm{~m}\) high and (a) \(100 \mathrm{~m}\) and (b) \(10.0 \mathrm{~m}\) behind the truck mirror?

The front surface of a glass cube \(5.00 \mathrm{~cm}\) on each side is placed a distance of \(30.0 \mathrm{~cm}\) in front of a converging mirror that has a focal length of \(20.0 \mathrm{~cm} .\) (a) Where is the image of the front and back surface of the cube located, and what are the image characteristics? (b) Is the image of the cube still a cube?

Two students in a physics laboratory each have a concave mirror with the same radius of curvature, \(40 \mathrm{~cm}\). Each student places an object in front of their mirror. The image in both mirrors is three times the size of the object. However, when the students compare notes, they find that the object distances are not the same. Is this possible? If so, what are the object distances?

When an object is moved closer to a convex mirror, its image size (1) increases, (2) remains the same, (3) decreases. Prove your answer mathematically.

An object is placed \(50.0 \mathrm{~cm}\) in front of a converging lens of focal length \(10.0 \mathrm{~cm} .\) What are the image distance and the lateral magnification?

An object placed \(30 \mathrm{~cm}\) in front of a converging lens forms an image \(15 \mathrm{~cm}\) behind the lens. What are the focal length of the lens and the lateral magnification of the image?

A converging lens with a focal length of \(20 \mathrm{~cm}\) is used to produce an image on a screen that is \(2.0 \mathrm{~m}\) from the lens. What are the object distance and the lateral magnification of the image?

When an object is placed at \(2.0 \mathrm{~m}\) in front of a diverging lens, a virtual image is formed at \(30 \mathrm{~cm}\) in front of the lens. What are the focal length of the lens and the lateral magnification of the image?

An object \(4.0 \mathrm{~cm}\) tall is in front of a converging lens of focal length \(22 \mathrm{~cm}\). The object is \(15 \mathrm{~cm}\) away from the lens. (a) Use a ray diagram to determine whether the (2) upright or inverted, and image is (1) real or virtual, (3) magnified or reduced. (b) Calculate the image distance and lateral magnification.

(a) Design the lens in a single-lens slide projector that will form a sharp image on a screen \(4.0 \mathrm{~m}\) away with the transparent slides \(6.0 \mathrm{~cm}\) from the lens. (b) If the object on a slide is \(1.0 \mathrm{~cm}\) tall, how tall will the image on the screen be?

An object is placed in front of a concave lens whose focal length is \(-18 \mathrm{~cm}\). Where is the image located and what are its characteristics, if the object distance is (a) \(10 \mathrm{~cm}\) and (b) \(25 \mathrm{~cm}\) ? Sketch ray diagrams for each case.

A convex lens produces a real, inverted image of an object that is magnified 2.5 times when the object is \(20 \mathrm{~cm}\) from the lens. What are the image distance and the focal length of the lens?

A convex lens has a focal length of \(0.12 \mathrm{~m}\). Where on the lens axis should an object be placed in order to get (a) a real, magnified image with a magnification of 2.0 and (b) a virtual, magnified image with a magnification of \(2.0 ?\)

Using the thin lens equation and the magnification factor, show that for a spherical diverging lens, the image of a real object is always virtual, upright, and reduced.

A simple single-lens camera (convex lens) is used to photograph a man \(1.7 \mathrm{~m}\) tall who is standing \(4.0 \mathrm{~m}\) from the camera. If the man's image fills the height of a frame of film \((35 \mathrm{~mm}),\) what is the focal length of the lens?

An object \(5.0 \mathrm{~cm}\) tall is \(10 \mathrm{~cm}\) from a concave lens. The resulting virtual image is one-fifth as large as the object. What is the focal length of the lens and the image distance?

An object is placed \(80 \mathrm{~cm}\) from a screen. (a) At what point from the object should a converging lens with a focal length of \(20 \mathrm{~cm}\) be placed so that it will produce a sharp image on the screen? (b) What is the image's magnification?

(a) If a book is held \(30 \mathrm{~cm}\) from an eyeglass lens with a focal length of \(-45 \mathrm{~cm}\), where is the image of the print formed? (b) If an eyeglass lens with a focal length of \(+57 \mathrm{~cm}\) is used, where is the image formed?

To correct hyperopia (farsightedness), convex lenses are prescribed. If a senior citizen can read a newspaper only when he holds it no closer than \(50 \mathrm{~cm}\) away, what focal length of lens should be prescribed so he can read when he holds the newspaper \(25 \mathrm{~cm}\) away?

A biology student wants to examine a bug at a magnification of +5.00 (a) The lens should be (1) convex, (2) concave, (3) flat. Explain. (b) If the bug is \(5.00 \mathrm{~cm}\) from the lens, what is the focal length of the lens?

The human eye is a complex multiple-lens system. However, it can be approximated to an equivalent single converging lens with an average focal length about \(1.7 \mathrm{~cm}\) when the eye is relaxed. If an eye is viewing a 2.0 -m-tall tree located \(15 \mathrm{~m}\) in front of the eye, what are the height and orientation of the image of the tree on the retina?