Draw ray diagrams to show how a convex lens can produce (a) a real image that is smaller than th

Draw ray diagrams to show how a convex lens can produce (a)...

Key Concepts

Virtual Image Formation

A virtual image occurs when the diverging light rays appear to originate from a point behind the lens, even though they do not actually converge there. In a convex lens, if an object is placed within the focal length, the rays after refracting diverge, and an observer perceives them as coming from an image that is erect and magnified. Virtual images cannot be projected on a screen, as they exist only by perception.

Real Image Formation

A real image is formed when light rays converge at a point after passing through a lens or reflecting off a mirror. In the case of a convex lens, when the object is placed outside the focal length, the lens converges the rays to produce an image that can be projected onto a screen. This image can be inverted and its size relative to the object depends on the object’s distance from the lens, resulting in images that are either larger or smaller than the object.

Magnification

Magnification in optics is the measure of how much larger or smaller an image is compared to the object, and it is calculated by the ratio of the image distance to the object distance. In a convex lens system, the magnification determines if a real image is larger or smaller than the object depending on the object’s placement relative to the focal length. This concept plays an important role in designing optical devices where maintaining the desired image size is critical.

Convex Lens

A convex lens, also known as a converging lens, is a transparent optical device with at least one curved surface that causes incoming parallel light rays to converge to a focal point. Its behavior under the lens-maker's equation enables it to form images by bending light, making it essential for applications ranging from magnifying glasses to corrective eyewear and cameras.

Ray Diagrams

Ray diagrams are schematic representations used in geometrical optics to illustrate the paths taken by light rays as they pass through optical devices like lenses and mirrors. They provide a visual tool to determine the location, size, orientation, and type (real or virtual) of the images formed, aiding in the conceptual understanding of how optical systems function.

Transcript

00:02 Hi, in the given problem, we have to show the formation of a real and diminished image, a real and a magnified image, and a virtual image with the help of a convex lens.

00:18 So, first of all, we have to obtain a real and diminished image.

00:27 So to get it, we should put the object in front of the convex lens at a distance from its optical center more than twice of its focal length.

00:50 So to show the image formation, first of all, we consider a point as an optical center of the lens.

01:01 Then we mark second principal focus and first principal focus having the same distances from optical center.

01:16 Then we mark twice of second principal focus and twice of the first principal focus.

01:27 Then finally we draw a convex lens like this.

01:38 Then we put an object in front of this convex lens at a distance from this optical center more than twice of its focal length.

01:54 Here this is the object, which should be shown with the help of an arrow drawn exactly perpendicular to the principal axis.

02:05 This is a, b, an arrow representing the object.

02:09 Now, to show the ray tracing, the first ray is taken starting from point b and traveling parallel to the principal axis, which passes through the principal focus.

02:24 First principal focus after refraction through the lens.

02:30 Then we take another ray passing through the optical center, which passes undeviated.

02:37 So finally we get an image there where the rays are intersecting after the refraction.

02:49 This is a -b -d -dash the real image of the object but diminished in size and invert it.

03:00 Now we have to obtain a real and magnified image.

03:04 So to get it, a real and magnified image.

03:19 To get it, we should put the object anywhere between the focus, second principal focus, and the twice of the second principal focus.

03:31 So again, to draw it, we begin with the principal axis.

03:36 Here, this is the principal axis...

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