Physics 1100 In-Class Problems: Optics

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 traveling 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. 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.
   
   
   
   

4. 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.
   

5. 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.
   

6. 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.
   

7. A beam of sunlight encounters a plate of crown glass at an angle of 45.00°. If the index of refraction for red light in crown glass is n_r = 1.520 and for violet light is n_v = 1.538, find the angle between the violet ray and the red ray in the glass.
   

8. A beam of light is incident at an angle θ = 40.0° on a triangular prism of angle α = 45.0° and index n = 1.50 as shown below. Find the angle β at which it emerges.
   
   

9. A silver medallion is sealed within a transparent block of plastic. An observer in air , viewing the medallion from directly above, sees the medallion at an apparent depth of 1.6 cm beneath the top surface of the medallion. How far below the top surface would the medallion appear if the observer (not wearing goggles) and the block were under water?
   

10. A ray of light is incident at 35.0° on a 5.00 mm thick plane of glass with refractive index n = 1.70. What is the displacement of the ray?
    

11. To determine the refractive index of a transparent material, its critical angle is measured in air. If θc = 40.5°, what is the index of refraction of the solid?
    

12. A point source of light is submerged 2.2 m below the surface of a lake and emits rays in all directions. On the surface of the lake, directly above the source, the area illuminated is a circle. What is the maximum radius that this circle could have?
    

13. 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.
    

    

14. 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.
    

    

15. 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?

16. 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?
    

Questions? mike.coombes@kwantlen.ca