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Chapter 23: Problem 59

Sketch a ray diagram to show that when an object is placed at twice the focal length from a converging lens, the image formed is inverted, real, and the same size as the object.

Short Answer

Expert verified
Question: Sketch a ray diagram for a converging lens with an object placed at a distance equal to twice the focal length. Describe the properties of the image formed. Answer: The image formed by the converging lens is real, inverted, and has the same size as the object. This is illustrated in the ray diagram, where the rays parallel to the optic axis and passing through the center of the lens intersect at the same place. The object is placed at a distance equal to twice the focal length, making the image formed at the same distance on the opposite side of the lens.

Step by step solution

01

Draw the optic axis, lens, and object

Start by drawing a straight horizontal line, which represents the optic axis. Then draw a converging lens at the center of the axis. Place an object (arrow representing the object is fine) on the optic axis at a distance equal to twice the focal length.
02

Draw the focal points and locate the object

Draw two points on the optic axis on either side of the lens to represent the focal points (F1 and F2). As we mentioned earlier, the object should be placed at a distance equal to twice the focal length, which means the object is located between F1 and double the distance from the lens to F1.
03

Draw a ray parallel to the optic axis from the top of the object

Draw a straight line (ray) from the top of the object parallel to the optic axis. This ray will pass through the lens and refract (bend) through the focal point (F2) on the other side.
04

Draw a ray passing through the center of the lens from the top of the object

Draw another ray from the top of the object through the exact center of the lens. This ray will not refract (bend) and will continue in a straight path.
05

Find the intersection of the rays

The image will be formed where the two rays (from Step 3 and Step 4) intersect on the opposite side of the lens. Draw an arrow from the intersection point down to the optic axis. This will represent the image.
06

Analyze the ray diagram

Notice that the image is formed on the opposite side of the object, making it real. Also, the image is inverted, as the arrow is pointing downward. Since the object was placed at twice the focal length, the image will be formed at the same distance (but on the other side of the lens), and the size of the image will be equal to the size of the object. This verifies the statements in the exercise.

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