Problem set 1 Due date: 6/4/1433 H Problem 1: The figure shows an over-head view of a corridor with a plane mirror M mounted at one end. A burglar B sneaks along the corridor directly toward the center of the mirror. If d = 3.0 m, how far from the mirror will she be when the security guard S can first see her in the mirror? Problem 2: In the figure, a real inverted image I of an object O is formed by a certain lens (not shown); the objectimage separation is d = 40.0 cm, measured aong the central axis of the lens. The image is just half the size of the object. (a) What kind of the lens must be used to produce this image? (b) How far from the object must the lens be placed? (c) What is the focal length of the lens? Problem 3: In the figure (a), a beam of light in material 1 is incident on a boundary at an angle of 30o. The extent to which the light is bent due to refraction depends, in part, on the index of refraction n2 of material 2. Figure (b) gives the angle of refraction 2 versus n2 for a range of possible n2 values, from na = 1.30 to nb=1.90. What is the speed of light in material 1? Problem 4: In about 1965, engineers at the Toro Company invented a gasoline gauge for small engines, diagrammed in (Fig 43 p. 1134). The gauge has no moving parts. It consists of a flat slab of transparent plastic fitting vertically into a slot in the cap on the gas tank. None of the plastic has a reflective coating. The plastic projects from the horizontal top down nearly to the bottom of the opaque tank. Its lower edge is cut with facets making angles of 45o with the horizontal. A lawnmower operator looks down from aboce and sees a boundary between bright and dark on the gauge. The location of the boundary, across the width of the plastic, indicates the quantity of gasoline in the tank. Explain how the gauge works. Explain the design requirements, if any, for the index of refraction of the plastic.