reflection physics problem solving

Physics Problems with Solutions

Reflection of light rays, examples and solutions, reflection of light rays on a reflecting surface.

Laws of reflection

(1) The incident light ray, the reflected light ray and the normal to the interface at the point of incidence make a plane called the plane of incidence (2) The angle of incidence i and the angle of reflection r have the same size.

A light ray strikes a reflective plane surface at an angle of 56° with the surface. a) Find the angle of incidence. b) Find the angle of reflection. c) Find the angle made by the reflected ray and the surface. d) Find the angle made by the incident and reflected rays.

question 1 - Reflection of Light Rays on a Reflecting Surface

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Learning Objectives

By the end of this section, you will be able to:

Whenever we look into a mirror, or squint at sunlight glinting from a lake, we are seeing a reflection. When you look at a piece of white paper, you are seeing light scattered from it. Large telescopes use reflection to form an image of stars and other astronomical objects.

The law of reflection states that the angle of reflection equals the angle of incidence, or

The law of reflection is illustrated in Figure 1.5 , which also shows how the angle of incidence and angle of reflection are measured relative to the perpendicular to the surface at the point where the light ray strikes.

A light ray is incident on a smooth surface and is making an angle theta i relative to a line drawn perpendicular to the surface at the point where the incident ray strikes it. The reflected light ray makes an angle theta r with the same perpendicular drawn to the surface. Both incident and reflected ray are on the same side of the surface but opposite sides of the perpendicular line.

We expect to see reflections from smooth surfaces, but Figure 1.6 illustrates how a rough surface reflects light. Since the light strikes different parts of the surface at different angles, it is reflected in many different directions, or diffused. Diffused light is what allows us to see a sheet of paper from any angle, as shown in Figure 1.7 (a). People, clothing, leaves, and walls all have rough surfaces and can be seen from all sides. A mirror, on the other hand, has a smooth surface (compared with the wavelength of light) and reflects light at specific angles, as illustrated in Figure 1.7 (b). When the Moon reflects from a lake, as shown in Figure 1.7 (c), a combination of these effects takes place.

The figure shown parallel light rays falling on a rough surface. The rays hit the surface at different angles to the perpendicular lines to the surface at the points of incidence, and the reflected rays get scattered in different directions.

When you see yourself in a mirror, it appears that the image is actually behind the mirror ( Figure 1.8 ). We see the light coming from a direction determined by the law of reflection. The angles are such that the image is exactly the same distance behind the mirror as you stand in front of the mirror. If the mirror is on the wall of a room, the images in it are all behind the mirror, which can make the room seem bigger. Although these mirror images make objects appear to be where they cannot be (like behind a solid wall), the images are not figments of your imagination. Mirror images can be photographed and videotaped by instruments and look just as they do with our eyes (which are optical instruments themselves). The precise manner in which images are formed by mirrors and lenses is discussed in an upcoming chapter on Geometric Optics and Image Formation .

Figure a is a drawing of a girl standing in front of a mirror and looking at her image. The mirror is about half as tall as the girl, with the top of the mirror above her eyes but below the top of her head. The light rays from her feet reach the bottom of the mirror and reflect to her eyes following the law of reflection: the angle of incidence theta is equal to the angle of reflection theta. The rays from the top of her head reach the top of the mirror and reflect to her eyes. Figure b is a drawing of the same girl looking at her twin. The twin is facing her and is at the same location, relative to her, that her image is in figure a. The rays from the twin’s feet and head travel directly to the girl’s eyes, reaching them in the same direction as the reflected rays in figure a.

Corner Reflectors (Retroreflectors)

A light ray that strikes an object consisting of two mutually perpendicular reflecting surfaces is reflected back exactly parallel to the direction from which it came ( Figure 1.9 ). This is true whenever the reflecting surfaces are perpendicular, and it is independent of the angle of incidence. (For proof, see [link] at the end of this section.) Such an object is called a corner reflector , since the light bounces from its inside corner. Corner reflectors are a subclass of retroreflectors, which all reflect rays back in the directions from which they came. Although the geometry of the proof is much more complex, corner reflectors can also be built with three mutually perpendicular reflecting surfaces and are useful in three-dimensional applications.

Two mirrors meet each other at a right angle. An incoming ray of light is reflected by one mirror and then the other, such that the outgoing ray is parallel to the incoming ray.

Many inexpensive reflector buttons on bicycles, cars, and warning signs have corner reflectors designed to return light in the direction from which it originated. Rather than simply reflecting light over a wide angle, retroreflection ensures high visibility if the observer and the light source are located together, such as a car’s driver and headlights. The Apollo astronauts placed a true corner reflector on the Moon ( Figure 1.10 ). Laser signals from Earth can be bounced from that corner reflector to measure the gradually increasing distance to the Moon of a few centimeters per year.

Figure a is a photograph of an astronaut placing a corner reflector on the moon. Figure b is a photograph of two bicycle safety reflectors.

Working on the same principle as these optical reflectors, corner reflectors are routinely used as radar reflectors ( Figure 1.11 ) for radio-frequency applications. Under most circumstances, small boats made of fiberglass or wood do not strongly reflect radio waves emitted by radar systems. To make these boats visible to radar (to avoid collisions, for example), radar reflectors are attached to boats, usually in high places.

A photograph of a radar reflector on the rigging of a sailboat.

As a counterexample, if you are interested in building a stealth airplane, radar reflections should be minimized to evade detection. One of the design considerations would then be to avoid building 90 ° 90 ° corners into the airframe.

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Ray Optics: Reflection and Mirrors

Calculator pad, version 2, reflection and mirrors: problem set.

A light ray approaches a mirror at an angle of incidence of 25°. What is the angle of reflection?

A light ray approaches a mirror at an angle of 22° with the mirror surface. What is the angle of reflection of this light ray?

Angle B = 38° Angle C = 52° Angle D = 38°

Anna Litical is doing the Plane Mirror Lab in physics class. She places a pin a distance of 4.9 cm from a plane mirror. How far behind the mirror can the image be expected to appear?

Baldwin Young stands 68 cm from his dresser mirror, inspecting his scalp. How far is the image of his scalp located from his scalp?

A meter stick (object) is placed in an upright position in front of a plane mirror as shown in the diagram at the right. The image of the meter stick is equidistant from the mirror. Suppose that the meter stick is equipped with a working eyeball capable of viewing the top and the bottom of its image. The eyeball is located at the 90-cm mark on the meter stick. Using either a ray diagram or geometry, determine … a. … the location of the intersection of the eye's line of sight with the mirror as the eyeball sights at the top of the image. b. … the location of the intersection of the eye's line of sight with the mirror as the eyeball sights at the bottom of the image. c. … the amount of mirror required by the meter stick to view the image.

a. 95 cm b. 45 cm c. 50 cm

A spherical concave mirror has a radius of curvature of +62 cm. What is the focal length of the mirror?

A decorative garden sphere has a diameter of 44 cm. The reflecting surface of the shiny sphere makes a great convex mirror. What is the focal point of the convex surface?

In a physics demonstration, a concave mirror having a 50.0 cm focal length is used to create images of a candle located at various locations along its principal axis. Beginning from a distance of several meters from the mirror, a candle is moved forward and its image is projected onto an opaque screen. Determine the image distances (distance from mirror to image) for object distances (distance from object to mirror) of … a. … 125.0 cm b. … 100.0 cm c. … 75.0 cm d. … 50.0 cm (Be careful with your math; the result is surprising.) e. … 25.0 cm

a. 83.3 cm b. 100.0 cm c. 150.0 cm d. No image. A solution to the mirror equation does not exist for this object distance. e. -50.0 cm

Problem 10:

Obtaining a large spherical mirror with a focal length of 0.654 m from the Physics Storeroom, Mr. H takes his last period class outside for a fascinating demo. A student volunteer holds the mirror at an angle such that the face of the mirror is directed towards the Sun - roughly 1.46x10 11 m away. Mr. H then uses a piece of paper with George Washington's picture on it to focus the image of the sun on the sheet of paper. Before the paper engulfs in flames, a bright image of the sun can be seen on the paper. Use the mirror equation to calculate the distance from the mirror to the image of the sun.

Problem 11:

Every morning Bob Gillette uses a shaving mirror with a focal length of 72 cm to view the image of his face. Supposing his face is 18 cm from the mirror, determine the image distance and the magnification of his face.

d i = -24 cm Magnification = 1.33

Problem 12:

The infamous Chinese magician Foo Ling Yu places a 56-mm tall light bulb a distance of 124 cm from a spherical concave mirror with a focal length of 62 cm. a. Determine the image distance and image height. b. Describe the orientation and type of the image.

a. d i = 124 cm and h i = -56 mm b. The image is inverted and real.

Problem 13:

In a physics lab, Anna Litical and Noah Formula position a small night light bulb at several locations along the principal axis of a concave mirror. Using a note card, they locate the image of the light bulb. The mirror has a focal length of 32.0 cm. What image distances would you expect Anna and Noah to observe when the object is located at distances of … a. … 85.3 cm from the mirror? b. … 64.0 cm from the mirror? c. … 48.1 cm from the mirror?

a. 51.2 cm b. 64.0 cm c. 95.6 cm

Problem 14:

Ima Primpin uses a cosmetic mirror to magnify her eyelashes during the traditional morning painting session. Her 1.2-cm long eyelashes are magnified to 1.6 cm when placed 5.8 cm from the mirror. a. Determine the image distance for such an upright image. b. Determine the focal length of the mirror.

a. -7.7 cm b. 23.2 cm

Problem 15:

In the Fall of 2006, the Sky Mirror sculpture was opened in Rockefeller Center in New York City. Standing three stories tall and weighing 23 tons, its concave side faced the Rockefeller Center and its convex side faced Fifth Avenue. a. A taxi on Fifth Avenue is located 38 m from the convex side of the sculpture and its image is one-fifth the size of the taxi. Determine the focal length of the mirror. b. Estimate the image size and image distance of the 260-m tall Rockefeller Center if it is located an estimated distance of 95 meters from the concave mirror surface. Assume the focal length of the concave side is the same magnitude as the focal length of the convex side.

a. -9.5 m b. d i = 11 m (rounded from 10.55 m) and h i = -29 m (- indicates inverted image)

Problem 16:

A convex spherical mirror has a focal point located a distance of 24.6 cm from the surface of the mirror. (You will have to decide for yourself whether f is + or -.) a. Find the image distance (in cm) for an object distance of 76.8 cm. b. Determine the magnification of this image.

a. d i = -18.6 cm b. M = 0.243

Problem 17:

A convenient store mounts a convex mirror in the corner of the store to serve as a security mirror and reduce the frequency of five-finger discounts . When Robin Storz is positioned a distance of 4.8 m from the mirror, her image is magnified by a factor of one-half. Determine the focal length of the mirror.

Problem 18:

Kerry Uss is studying the convex side of her soup spoon. She notices that her 3.8-cm tall nose appears to be 1.2 cm tall when positioned a distance of 2.4 cm from the spoon. a. Determine the image distance for this particular object distance. b. Determine the focal length of the convex side of the spoon.

a. d i = -0.76 cm b. f = -1.1 cm

Problem 19:

A large spherical mirror sculpture is constructed in the town square at Physicston, Illinois. The sculpture consists of a large sphere with a diameter of 24 meters which is coated with a reflecting material. A 1.8 meter tall photographer stands a distance of 38 m from the concave side of the sculpture and takes a picture. Determine the image distance and the magnification of the photographer.

d i = 7.1 m Mag = -0.19

Problem 20:

Baxter Nachure lives in the country along Sinewave road. It is difficult to pull out of the driveway onto the road since the road is curved and trees prevent him from seeing around the corner. He recently installed a large convex mirror at one of the curves to give him a wider angle of view. It has a focal length of -1.54 meters. Determine the magnification of an oncoming car located 35.8 m from the mirror.

Problem 21:

A virtual image is formed 26.9 cm from a concave mirror having a radius of curvature of 48.1 cm. Determine the object distance.

Problem 22:

An 4.9-cm tall object is positioned 14.8 cm from a mirror. Determine the radius of curvature which the mirror must have in order to produce an upright image that is 7.2 cm tall?

Problem 23:

A dentist uses a spherical mirror to produce an upright image of a patient's tooth which is magnified by a factor of 4.5 when placed 1.8 cm from the tooth. (a) What type of mirror - concave or convex - is being used? (b) What is the focal length of the mirror?

a. Concave mirror. Convex mirrors do not magnify the image; they only reduce the image. b. 2.3 cm

Problem 24:

The real image produced by a concave mirror is observed to be six times larger than the object when the object is 34.2 cm in front of a mirror. Determine the radius of curvature of this mirror.

Problem 25:

A shiny bauble (ornament) hangs on Mr. H's Christmas tree. The bauble has a radius of 4.8 cm. Matthew looks into the bauble and observes an image of his face which is one-eighth the size of his face. How far from the bauble is Matthew's face?

Problem 26:

A child at an amusement park stands in front of a concave mirror with a focal length of 73.9 cm. With great amusement, the child holds her cotton candy close to the mirror and observes that its image is magnified by a factor of five. Determine the object distance which creates this magnification of five.

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IMAGES

How to solve Reflection calculations
Example Of Reflection And Refraction
Physics Reflection & Refraction AQA GCSE Lesson
Light Reflection
Refraction and Critical Angles Calculator
What causes reflection? + Example

VIDEO

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COMMENTS

16.1 Reflection
Explain reflection from mirrors, describe image formation as a consequence of reflection from mirrors, apply ray diagrams to predict and interpret image and object locations, and describe applications of mirrors. Perform calculations based on the law of reflection and the equations for curved mirrors.
Reflection of Light Rays, Examples and Solutions
by law of reflection : r = i and r' = i' Substitute to obtain i + i + i' + i' = 180 ° i + i' = 90 In triangle AOB, we have α + (90 - r) + (90 - i') = 180 ° α = r + i' = i + i' = 90 ° If α = 90 °, the incident ray at A and the reflected ray at B are parallel. More References and Links Reflection of Light Rays, Examples and Solutions. More Info
1.2 The Law of Reflection
The law of reflection states that the angle of reflection equals the angle of incidence, or. The law of reflection is illustrated in Figure 1.5, which also shows how the angle of incidence and angle of reflection are measured relative to the perpendicular to the surface at the point where the light ray strikes.