In Figure P36.50, a thin converging lens of focal length

Chapter 36, Problem 50

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In Figure P36.50, a thin converging lens of focal length 14.0 cm forms an image of the square abcd, which is hc 5 hb 5 10.0 cm high and lies between distances of pd 5 20.0 cm and pa 5 30.0 cm from the lens. Let a9, b9, c9, and d9 represent the respective corners of the image. Let qa represent the image distance for points a9 and b9, qd represent the image distance for points c9 and d9, h9 b represent the distance from point b9 to the axis, and h9c represent the height of c9. (a)Find qa , qd , h9 b, and h9 c. (b) Make a sketch of the image. (c) The area of the object is 100 cm2. By carrying out the following steps, you will evaluate the area of the image. Let q represent the image distance of any point between a9 and d9, for which the object distance is p. Let h9 represent the distance from the axis to the point at the edge of the image between b9 and c9 at image distance q. Demonstrate that 0 hr 0 5 10.0q a 1 14.0 2 1 q b where h9 and q are in centimeters. (d) Explain why the geometric area of the image is given by 3 qd q a 0 hr 0 dq (e) Carry out the integration to find the area of the image.