Chapter 23

Mirrors and Lenses Conceptual questions: 4,5,10,14,15,17 Quick Quizzes: 1,2,4,6 Problems: 17,44,53,61

Types of Images for Mirrors and Lenses

  A real image is one in which light actually passes through the image point  Real images can be displayed on screens A virtual image is one in which the light does not pass through the image point  Virtual images cannot be displayed on screens

Flat Mirror

 The object distance is the distance from the object to the mirror or lens  Denoted by p  The image distance is the distance from the image to the mirror or lens  Denoted by q  The lateral magnification of the mirror or lens is the ratio of the image height to the object height  Denoted by M

QUICK QUIZ 23.1

In the overhead view of the figure below, the image of the stone seen by observer 1 is at

C

. Where does observer 2 see the image ––at

A

, at

B

, at

C

, at D, at

E

, or not at all?

Day and Night Settings on Auto Mirrors

Concave Mirror

    The mirror has a of curvature of R radius Its center of curvature the point C is Point V is the center of the spherical segment A line drawn from C to V is called the of the mirror principle axis

Image Formed by a Concave Mirror  Geometry shows the relationship between the image and object distance is 1  p 1  q 2 R  Magnification is M  h h '   q p  h’ is negative when the image is inverted with respect to the object

Focal Length Shown by Parallel Rays

Focal Length

 Focal length, the distance between the focal point and the mirror, is half the radius f = R / 2  The mirror equation can be expressed as 1  p 1 q  1 f

Convex Mirrors

A convex mirror is also called a mirror diverging

Ray Diagram

   Ray 1 is drawn parallel to the principle axis and is reflected back through the focal point, F Ray 2 is drawn through the focal point and is reflected parallel to the principle axis Ray 3 is drawn through the center of curvature and is reflected back on itself

Ray Diagram for Concave Mirror, p > R

Based on conceptual question 17

Draw a ray diagram for a. a convex mirror b. a concave mirror with the object at a distance p>R

Ray Diagram for a Convex Mirror

Ray Diagram for a Concave Mirror, p < f

True or false?

(a) The image of an object placed in front of a concave mirror is always upright. (b) The height of the image of an object placed in front of a concave mirror must be smaller than or equal to the height of the object. (c) The image of an object placed in front of a convex mirror is always upright and smaller than the object.

Problem 17

 A child holds a candy bar 10.0 cm in front of a convex mirror and notices that the image is only one-half the size of the candy bar. What is the radius of curvature of the mirror?

Images Formed by Refraction

 When n 2 > n 1 , Object distance, image distance and radius of curvature are related by the equation:

n p

1 

n q

2 

n

2 

n

1

R

M  h ' h   n 1 q n 2 p   Real images are formed on the side opposite from the object Sign conventions – Table 23.2

Sign convention for refracting surfaces

Flat Refracting Surface

 The image and the object are on the side of the surface. The image is virtual same

QUICK QUIZ 23.2

A person spear fishing from a boat sees a fish located 3 m from the boat at an apparent depth of 1 m. To spear the fish, should the person aim (a) at, (b) above, or (c) below the image of the fish?

Problem 53

A parallel beam of light enters a glass hemisphere perpendicular to the flat face, as shown in Figure P23.53. The radius is R = 6.00 cm, and the index of refraction is n = 1.560. Determine the point at which the beam is focused. (Assume paraxial rays; that is, all rays are located close to the principal axis.)

Conceptual question

 10. Why does a clear stream appear to be shallower than it actually is?

Atmospheric Refraction and Mirages

   A mirage can be observed when the air above the ground is warmer than the air at higher elevations The rays in path B are directed toward the ground and then bent by refraction The observer sees both an upright and an inverted image

Thin Lens Shapes

   These are examples of converging lenses They have positive focal lengths They are thickest in the middle

Thin Diverging Lenses

   These are examples of diverging lenses They have negative focal lengths They are thickest at the edges

Lens Equations

 The geometric derivation of the equations is very similar to that of mirrors M  h ' h   q p 1  p 1 q  1 f

Sign Conventions for Thin Lenses Quantity Positive When Negative When Object location (p) Image location (q) Image height (h’) Object is in front of the lens Image is in back of the lens Image is upright Object is in back of the lens Image is in front of the lens Image is inverted R 1 and R 2 Focal length (f) Center of curvature is in back of the lens Center of curvature is in front of the lens Converging lens Diverging lens

The Lens Maker’s formulae

f 1  ( n  1 )   1 R 1  1 R 2  

Ray Diagrams for Thin Lenses

   The first ray is drawn parallel to the first principle axis and then passes through (or appears to come from) one of the focal lengths The second ray is drawn through the center of the lens and continues in a straight line The third ray is drawn from the other focal point and emerges from the lens parallel to the principle axis

Ray Diagram for Converging Lens, p > f

  The image is real The image is inverted

Ray Diagram for Converging Lens, p < f

  The image is virtual The image is upright

Ray Diagram for Diverging Lens

  The image is virtual The image is upright

Conceptual questions

  5. You are taking a picture of yourself with a camera that uses an ultrasonic range finder to measure the distance to the object. When you take a picture of yourself in a mirror with this camera, your image is out of focus. Why?

14. Lenses used in sunglasses whether converging or diverging, are always designed such that the middle of the lens curves away from the eye. Why?

QUICK QUIZ 23.4

A plastic sandwich bag filled with water can act as a crude converging lens in air. If the bag is filled with air and placed under water, is the effective lens (a) converging or (b) diverging?

QUICK QUIZ 23.6

An object is placed to the left of a converging lens. Which of the following statements are true and which are false? (a) The image is always to the right of the lens. (b) The image can be upright or inverted. (c) The image is always smaller or the same size as the object.

Combination of Thin Lenses, example



Problem 44.

Two converging lenses having focal lengths of 10.0 cm and 20.0 cm are placed 50.0 cm apart, as shown in Figure. The final image is to be located between the lenses, at the position indicated. (a) How far to the left of the first lens should the object be positioned? (b) What is the overall magnification? (c) Is the final image upright or inverted?

Problem 61

(a) The lens maker’s equation for a lens with index n 1 immersed in a medium with index n 2 takes the form 1/f=(n 1 /n 2 -1)(1/R 1 -1/R 2 ) A thin diverging glass lens (index = 1.50) with R 1 = –3.00 m and the lens. R 2 = –6.00 m is surrounded by air. An arrow is placed 10.0 m to the left of Determine the position of the image. (b) (c) Repeat with the arrow and lens immersed in water (index = 1.33); a medium with an index of refraction of 2.00.

Spherical Aberration

  Results from the focal points of light rays far from the principle axis are different from the focal points of rays passing near the axis For a mirror, parabolic shapes can be used to correct for spherical aberration

Chromatic Aberration

  Different wavelengths of light refracted by by a lens focus at different points   Violet rays are refracted more than red rays The focal length for red light is greater than the focal length for violet light Chromatic aberration can be minimized by the use of a combination of converging and diverging lenses

Conceptual questions

Question 4. Explain why a mirror cannot give rise to chromatic aberration.

Question 15. Why does a focal length of a mirror not depend on the mirror material when the focal length of a lens depends on the lens material?

True or false?

(a) The image of an object placed in front of a concave mirror is always upright. (b) The height of the image of an object placed in front of a concave mirror must be smaller than or equal to the height of the object. (c) The image of an object placed in front of a convex mirror is always upright and smaller than the object .

Review questions 1. What is the focal length of a flat mirror?

a. 0 b. positive c. infinite d. Negative 2. The magnification of a 3 cm object placed 5 cm from a certain lens is -1. What is the focal distance of the lens?

a. 0.4 cm b. 0.5 cm c. 2.5 cm d. 5.0 cm

3. Which of the following is responsible for mirage?

a. diffraction b. reflection c. refraction d. dispersion 4. An alligator sits 1 m below the surface of water of index of refraction n=1.4. The alligator’s view of objects above the surface is restricted to a circular window at the surface of radius a. 0.5 m c.

2 m b.

d.

1 m 2.6 m