Physics 1102 In-Class Problems: Images Formed by Mirrors and Lenses

1. Determine the minimum height of a wall mirror that will permit a 1.8-metre tall person to view his or her entire height. Sketch rays from the top and bottom of the person, and determine the proper placement of the mirror such that the full image is seen, regardless of the person's distance from the mirror.

2. Two plane mirrors are inclined to one another at an angle α. A ray travelling in the plane as shown below is incident on one of the mirrors. Applying the Law of Reflection, show that the path of the ray after the two reflections is deviated by an angle which is independent of the angle of incidence. Express your answer in terms of α.
   

3. In the diagram below are two plane mirrors set at an angle of 60° to one another. A point P is on the bisector of the angle between the two mirrors. Find all the possible images.
   

4. Three mirrors are arranged as in the diagram below. Find all the images of point P.
   
   

5. Use the Principle Ray Technique to find the image, created by a concave spherical mirror, of an object placed (a) between C and F, (b) at C, and (c) between F and the mirror. In each case, characterize the image, if possible.
   

   
   

   
   

   
   

6. When people stand in front of a type of mirror found in amusement parks, they see themselves with small heads and large lower torsos. Explain how this is accomplished.

7. An object is placed 25 cm in front of a concave mirror of focal length 30 cm. Calculate the image distance and the magnification. Characterize the image.

8. An object is placed 25 cm in front of a convex mirror of focal length 30 cm. Calculate the image distance and the magnification. Characterize the image.

9. Use the Principle Ray Technique to find the image, created by a converging lens, of an object placed between the first focal point F and the lens. Characterize the image.
   

   

10. Use the Principle Ray Technique to find the image, created by a diverging lens, of an object placed between F and the lens. Characterize the image.
    

    
    

11. The convex lens of a magnifying glass has a focal length of 20 cm. At what distance from the postage stamp must you hold this lens if the image of the stamp is to be twice as large as the stamp and
    (a) the image is inverted, or
    (b) the image is erect?
    

12. A lens forms an image of an object. The object is 20.0 cm from the lens. The image is 5.00 cm from the lens on the same side as the object.
    (a) What is the focal length of the lens? Is the lens converging or diverging?
    (b) If the object is 2.00 cm tall, how tall is the image? Is it erect or inverted?
    

13. An optical system comprises an object, of height 3 mm, fixed at a distance of 1.60 m from a screen. A converging lens can be moved freely in the space between the object and the screen. It is found that there are TWO positions of the lens which will give a real image on the screen, and that these two positions are 80 cm apart. Determine the focal length of the lens and the sizes of the two images. A neat diagram is required. Think about the symmetry of the problem.
    

14. Two converging lenses have focal lengths f₁ = 30 cm and f₂ = 20 cm. They are placed 60 cm apart along the same axis and an object is placed 50 cm from lens #1 on the side opposite lens #2. Locate the final image and calculate its overall magnification. State the final image characteristics relative to the original object. Sketch the ray diagram.
    

    

15. For the optical system shown below, determine the final image position as seen by the observer of the object at position O, due to the lenses and the plane mirror.

    

Questions? mike.coombes@kwantlen.ca