Video: Understanding How Convex Lenses Form Images

Which of the following types of images can be formed by the converging lens shown? (I) Real image, larger than the object (II) Real image, smaller than the object (III) Virtual image [A] I and III only [B] I and II only [C] III only [D] I, II, and III [E] I only

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Video Transcript

Which of the following types of images can be formed by the converging lens shown? Roman numeral (I) real image, larger than the object. Roman numeral (II) real image, smaller than the object. Roman numeral (III) virtual image. (a) Roman numerals I and III only. (b) Roman numerals I and II only. (c) Roman numeral III only. (d) Roman numerals I, II, and III. (e) Roman numeral I only.

To determine which type of images are possible from the converging lens, we can draw ray diagrams. Recall that there are three rules for drawing ray diagrams for a lens. Rule one, a ray that is parallel to the principal axis will pass through the focus. Rule two, a ray passing through the focus will become parallel to the principal axis. Rule three, a ray passing through optical center will not bend.

There are only three places that we can put our object in relation to the lens. One place that we can place our object is between the focal point and the lens. In our diagram, we have drawn our principal axis, which is the imaginary horizontal line that goes through the lens’s center. We have also included the focal points on either side of the lens, as represented by the letter F. Recall that the focal point is the point at which parallel rays incident on a lens will intersect. By applying the three rules for ray diagrams, we can determine which type of image is formed when an object is placed between the focal point and the lens.

Beginning with rule one, we draw a ray from the top of the object that is parallel to the principal axis, bends at the lens, and goes through the focal point on the other side. The second rule tells us to draw a ray that starts at the focal point, comes up through the object, bends at the lens, and becomes parallel to the principal axis on the other side. Our third ray starts at the top of the object, goes through the optical center, and continues in a straight line without bending. The image will form where all the rays intersect or converge together.

Looking at our diagram, we can see that our rays diverge from one another. Therefore, we must extend them back in the opposite direction to find where they intersect. Extending all of our rays back, we can see that they all converge at this point. This makes our image virtual, as it is on the same side of the lens as the object.

Looking back at our choices for the types of images that can be formed, we can see that the virtual image is Roman numeral (III). This means that we can eliminate any answer choice that does not include Roman numeral (III) as a possible image formed by the converging lens. Both answer choice (b) and (e) can be eliminated as they do not include Roman numeral III.

A second scenario is when our object is placed just outside the focal length of the lens. We once again apply our three rules for drawing ray diagrams. The first ray begins at the top of the object, is drawn parallel to the principal axis, bends at the lens, and goes through the focal point on the other side. The second rays comes off the top of the object, goes down through the focal point, bends at the lens, and becomes parallel to the principal axis on the other side. The third ray comes down off the top of the object through the optical center and continues straight without bending. Where the lines converge together is where the image will be formed. This is a real image as the image is on the opposite side of the lens to the object. The image is also larger than the object.

Looking back at our statements, Roman numeral (I) a real image, larger than the object is also a possible type of image formed by the converging lens. This means that our answer choice must contain both Roman numeral (I) and Roman numeral (III). We can eliminate answer choice (c), as it has only Roman numeral (III) in it. We must analyze our third placement for our object to determine whether answer choice (a) or (d) is correct.

In our third scenario, we place our object very far outside of the focal point. Our first ray comes off the top of the object parallel to the principal axis, bends at the lens, and comes through the focal point on the other side. The second ray comes off the top of the object down through the focal point, bends at the lens, and becomes parallel to the principal axis on the other side. The third ray comes down off the top of the object, goes through the optical center, and continues straight without bending. Where the lines converge is where the image will be formed.

This scenario once again produces an image that is real as the image is on the opposite side of the lens from the object. But we can see that the size of the image is smaller than the object. Looking back at Roman numeral (II), we can see from our third scenario that a real image smaller than the object is also a possibility. This means that our answer choice must contain all three statements, Roman numerals (I), (II), and (III). This would be answer choice (d).

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