Chapter 36, Problem 36.90AP

In a darkened room, a burning candle is placed 1.50 in from a white wall. A lens is placed between the candle and the wall at a location that causes a larger, inverted image to form on the wall. When the lens is in this position, the object distance is p₁. When the lens is moved 90.0cm toward the wall, another image of the candle is formed on the wall. From this information, we wish to find p₁ and the focal length of the lens. (a) From the lens equation for the first position of the lens, write an equation relating the focal length f of the lens to the object distance p₁, with no other variables in the equation. (b) From the lens equation for the second position of the lens, write another equation relating the focal length f of the lens to the object distance p₁. (c) Solve the equations in parts (a) and (b) simultaneously to find p₁. (d) Use the value in part (c) to find the focal length f of the lens.