A convex mirror (of focal length magnitude 6.0 cm) is place in combination with a converging lens (of focal length magnitude 8.0 cm). Assume the mirror is placed 9.0 cm to the left of the lens, and a small object is placed 12.0 cm to the right of the lens. If the origin of the coordinate system is placed at the location of the mirror and we set positive rightward, what is the position of the final image? Express your answer in cm, to at least one digit after the decimal point.

Two plane mirrors make the angle a = 33.0 degrees between them. A ray of light incident on one of the mirrors is reflected and it hits the second mirror. Find the angle between the ray incident on the first mirror and the ray reflected off of the second mirror.

For an independent study project, you design an experiment to measure the speed of light. You propose to bounce laser light off a mirror that is 51.5 km due east and have it detected by a light sensor that is 127 m due south of the laser. The first problem is to orient the mirror so that the laser light reflects off the mirror and into the light sensor. (a) Determine the angle that the normal to the mirror should make with respect to due west.   (b) Since you can read your protractor only so accurately, the mirror is slightly misaligned and the actual angle between the normal to the mirror and due west exceeds the desired amount by 0.004°. Determine how far south you need to move the light sensor in order to detect the reflected laser light.

38 A student wants to measure the height of a building. He walks out a distance of 48.5 m from its base and shining a flashlight beam towards the top. When the beam is elevated at an angle of 41.0° with respect to the horizontal, the beam just strikes the top of the building. If the flashlight is held at a height of 2.03 m, find the height of the building. * O