Section 3 Curved Mirrors. Calculate distances and focal lengths using the mirror equation for concave and convex spherical mirrors.

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Robert Harvey
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1 Objectives Calculate distances and focal lengths using the mirror equation for concave and convex spherical mirrors. Draw ray diagrams to find the image distance and magnification for concave and convex spherical mirrors. Distinguish between real and virtual images. Describe how parabolic mirrors differ from spherical mirrors.

2 Concave Spherical Mirrors A concave spherical mirror is a mirror whose reflecting surface is a segment of the inside of a sphere. Concave mirrors can be used to form real images. A real image is an image formed when rays of light actually pass through a point on the image. Real images can be projected onto a screen.

3 Image Formation by a Concave Spherical Mirror

4 Concave Spherical Mirrors, continued The Mirror Equation relates object distance (p), image distance (q), and focal length (f) of a spherical mirror. 1 p + 1 q = 1 f 1 object distance + 1 image distance = 1 focal length

5 Concave Spherical Mirrors, continued The Equation for Magnification relates image height or distance to object height or distance, respectively. magnification = M = h ' h = q p image height object height = image distance object distance

6 Concave Spherical Mirrors, continued Ray diagrams can be used for checking values calculated from the mirror and magnification equations for concave spherical mirrors. Concave mirrors can produce both real and virtual images.

7 Sample Problem Imaging with Concave Mirrors A concave spherical mirror has a focal length of 10.0 cm. Locate the image of a pencil that is placed upright 30.0 cm from the mirror. Find the magnification of the image. Draw a ray diagram to confirm your answer.

8 Sample Problem, continued Imaging with Concave Mirrors 1. Determine the sign and magnitude of the focal length and object size. f = cm p = cm The mirror is concave, so f is positive. The object is in front of the mirror, so p is positive.

9 Sample Problem, continued Imaging with Concave Mirrors 2. Draw a ray diagram using the rules for drawing reference rays.

10 Sample Problem, continued Imaging with Concave Mirrors 3. Use the mirror equation to relate the object and image distances to the focal length. 1 p + 1 q = 1 f 4. Use the magnification equation in terms of object and image distances. M = q p

11 Sample Problem, continued 5. Rearrange the equation to isolate the image distance, and calculate. Subtract the reciprocal of the object distance from the reciprocal of the focal length to obtain an expression for the unknown image distance. 1 q = 1 f 1 p

12 Sample Problem, continued Substitute the values for f and p into the mirror equation and the magnification equation to find the image distance and magnification. 1 q = cm cm = cm cm = cm q = 15 cm M = q 15 cm = p 30.0 cm = 0.50

13 Sample Problem, continued 6. Evaluate your answer in terms of the image location and size. The image appears between the focal point (10.0 cm) and the center of curvature (20.0 cm), as confirmed by the ray diagram. The image is smaller than the object and inverted ( 1 < M < 0), as is also confirmed by the ray diagram. The image is therefore real.

14 Image Formation by a Convex Spherical Mirror

15 Sample Problem Convex Mirrors An upright pencil is placed in front of a convex spherical mirror with a focal length of 8.00 cm. An erect image 2.50 cm tall is formed 4.44 cm behind the mirror. Find the position of the object, the magnification of the image, and the height of the pencil.

16 Sample Problem, continued Convex Mirrors Given: Because the mirror is convex, the focal length is negative. The image is behind the mirror, so q is also negative. f = 8.00 cm q = 4.44 cm h = 2.50 cm Unknown: p =? h =?

17 Sample Problem, continued Convex Mirrors Plan Choose an equation or situation: Use the mirror equation and the magnification formula. 1 p + 1 q = 1 f and M = h ' h = q p Rearrange the equation to isolate the unknown: 1 p = 1 f 1 q and h = p q h '

18 Sample Problem, continued Convex Mirrors 3. Calculate Substitute the values into the equation and solve: 1 p = cm cm 1 p = cm cm = cm p = 10.0 cm

19 Sample Problem, continued Convex Mirrors 3. Calculate, continued Substitute the values for p and q to find the magnification of the image. M = q p h = p q h = 5.63 cm 4.44 cm = 10.0 cm Substitute the values for p, q, and h to find the height of the object. h ' = 10.0 cm 4.44 cm M = (2.50 cm)

20 Practice Problems to be Completed Page 458 #1-4 Page 462 #1-4

Optics Practice. Version #: 0. Name: Date: 07/01/2010

Optics Practice. Version #: 0. Name: Date: 07/01/2010 Optics Practice Date: 07/01/2010 Version #: 0 Name: 1. Which of the following diagrams show a real image? a) b) c) d) e) i, ii, iii, and iv i and ii i and iv ii and iv ii, iii and iv 2. A real image is