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Chapter 23: Problem 60

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

Short Answer

Expert verified
Question: When an object is placed between twice the focal length and the focal length from a converging lens, describe the properties of the image formed. Answer: The image formed is inverted, real, and enlarged in size.

Step by step solution

01

Draw the lens, object, and focal points

First, draw a vertical line to represent the converging lens. Place a point F on each side of the lens to represent the focal points. Note that each focal length is the same, let it be f. Label a point O at a distance between f and 2f away from the lens on the left side as the object location.
02

Draw the principal rays

The three principal rays are: 1. Ray 1: A ray parallel to the principal axis from the top of the object to the lens. After passing through the lens, it goes through the focal point F on the right side. 2. Ray 2: A ray from the top of the object that passes through the center of the lens without any refraction. 3. Ray 3: A ray from the top of the object passing through the left focal point F, and after passing the lens, it becomes parallel to the principal axis.
03

Locate and draw the image

The point where the three principal rays meet after passing through the lens is the image location. Draw the image (label it as I) by connecting the intersection point to the principal axis. Note that Ray 2 and Ray 3 might not intersect in the diagram perfectly when drawn, but their extended lines will intersect.
04

Verify the image properties

Now, analyze the sketch to identify the image properties: 1. Inverted: The image I is located below the principal axis, so it is inverted. 2. Real: The three principal rays intersect at the image location. Since these rays physically converge at a point, the image is real. 3. Enlarged: Compare the height of the image I to the height of the object O. In this case, the image I is larger than the object, so the image is enlarged in size. The ray diagram now confirms that when an object is placed between twice the focal length and the focal length from a converging lens, the image formed is inverted, real, and enlarged in size.

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Most popular questions from this chapter

A beam of light in air is incident on a stack of four flat transparent materials with indices of refraction 1.20 \(1.40,1.32,\) and \(1.28 .\) If the angle of incidence for the beam on the first of the four materials is \(60.0^{\circ},\) what angle does the beam make with the normal when it emerges into the air after passing through the entire stack?
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.
Is there a critical angle for a light ray coming from a medium with an index of refraction 1.2 and incident on a medium that has an index of refraction \(1.4 ?\) If so, what is the critical angle that allows total internal reflection in the first medium?
Sketch a ray diagram to show that when an object is a distance equal to the focal length from a converging lens, the emerging rays from the lens are parallel to each other, so the image is at infinity.
An object is placed in front of a convex mirror with a 25.0 -cm radius of curvature. A virtual image half the size of the object is formed. At what distance is the object from the mirror? Draw a ray diagram to illustrate.
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