The focal length of the lens.

Question

You are working for an electronics company that makes devices for the home. Your supervisor has given you an assignment to help design the projection mechanism for a projection alarm clock. In this type of clock, a projection system is mounted on the body of the clock, as shown, where the projection system is the silver cylinder, of radius R = 3.25 cm, mounted on the left side of the clock. A converging lens is mounted on the edge of the cylinder. Inside the cylinder, a small digital display of the time in red characters can be moved from the center of the cylinder outward radially toward the lens. The red light of the digital display can be seen in the lens as shown. As a result, an image of the time is projected in red onto the ceiling or wall of a darkened room (as shown). The range of distances for focused images of the digital display is from 0.500 m to 4.00 m, measured from the center of the cylinder. For the smallest value of the range, the digital display is at the center of…

Answer 1

Question

Chapter 35, Problem 31P

(a)

To determine

The focal length of the lens.

(b)

To determine

The distance of the digital display from the centre of cylinder for the largest value of the range.

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You are working for an electronics company that makes devices for the home. Your supervisor has given you an assignment to help design the projection mechanism for a projection alarm clock. In this type of clock, a projection system is mounted on the body of the clock, as shown, where the projection system is the silver cylinder, of radius R = 3.25 cm, mounted on the left side of the clock. A converging lens is mounted on the edge of the cylinder. Inside the cylinder, a small digital display of the time in red characters can be moved from the center of the cylinder outward radially toward the lens. The red light of the digital display can be seen in the lens as shown. As a result, an image of the time is projected in red onto the ceiling or wall of a darkened room (as shown). The range of distances for focused images of the digital display is from 0.500 m to 4.00 m, measured from the center of the cylinder. For the smallest value of the range, the digital display is at the center of…

In Figure P35.30, a thin converging lens of focal length 14.0 cm forms an image of the square abed, which is h, h, = 10.0 cm high and lies between distances of p, = 20.0 cm and p. = 30.0 cm from the lens. Let a', b', c', and d' represent the respective corners of the image. Let q, rep- resent the image distance for points d' and b', q. represent the image dis- tance for points e' and d', h, represent the dis- tance from point b' to the axis, and H represent the height of c'. (a) Find q. 94, h, and h'. (b) Make a sketch of the image. (c) The area of the object is 100 cm?. By carrying out the following steps, you will evaluate the area of the image. Let q represent the image distance of any point between a' and d', for which the object distance is p. Let h' represent the dis- tance from the axis to the point at the edge of the image between i and c' at image distance q. Demonstrate that a dF Figure P35.30 |씨%=D10.0g( 14.0 9. where k and q are in centimeters. (d) Explain why the geo-…

30. In Figure P35.30, a thin converging lens of focal length QIC 14.0 cm forms an image of the square abcd, which is h, h, = 10.0 cm high and lies between distances of p, = 20.0 cm and p. = 30.0 cm from the lens. Let a', b', c', and d' represent the respective corners of the image. Let q, rep- resent the image distance for points a' and b', q. represent the image dis- tance for points e' and d', , represent the dis- tance from point b' to the axis, and h represent the height of c'. (a) Find g. Ie h, and h'. (b) Make a sketch of the image. (c) The area of the object is 100 cm?. By carrying out the following steps, you will evaluate the area of the image. Let q represent the image distance of any point between a' and d', for which the object distance is p. Let k' represent the dis- tance from the axis to the point at the edge of the image between b' and c' at image distance q. Demonstrate that a dF a Figure P35.30 |시= 10.0g 14.0