Use a ruler to draw ray diagrams to locate the images of the following objects: (a) an object th

Use a ruler to draw ray diagrams to locate the images of the...

Key Concepts

Magnification

Magnification refers to the ratio between the height of the image and the height of the object. It is determined by the distances of the object and the image from the lens. Magnification not only indicates the relative size but also whether the image is inverted or upright.

Real and Virtual Images

Real images are formed when light rays converge at a point and can be projected onto a screen, while virtual images are formed when the rays appear to diverge from a common point. In ray diagrams, real images are typically inverted relative to the object, and virtual images are upright.

Lens Equation

The lens equation, commonly written as 1/f = 1/do + 1/di, relates the focal length (f) of the lens to the object distance (do) and the image distance (di). This equation is essential for quantitatively predicting where the image will form and whether it will be real or virtual.

Ray Diagrams

Ray diagrams are graphical representations that use a few well-defined rays to locate the image formed by an optical system. In the context of lenses, key rays are drawn from the top of the object through the center of the lens, parallel to the principal axis, and towards the focal point, to determine the position, size, and orientation of the resultant image.

Focal Length

The focal length is the distance between the center of a lens and its focal point, where parallel rays converge after passing through the lens. It is a crucial parameter in determining the nature and position of the image formed by the lens.

Convex Lens

A convex lens, also known as a converging lens, is an optical device that bends incoming parallel rays towards a common point known as the focal point. It is widely used in image formation because it can produce either real or virtual images depending on the position of the object relative to its focal length.

Transcript

00:02 Hi, in the given problem there is a convex lens having a focal length of 10 centimeter.

00:10 We have to obtain the images of the objects kept in front of this convex lens at various distances.

00:19 So in the first part of the problem, the object has been kept at a distance of p is equal to 30 centimeter in front of this convex lens.

00:35 And as per sign convention, we can use it as minus 30 centimeter.

00:40 But we do not have to use any expression to find the image distance.

00:47 We have to actually use just the image formation.

00:52 So in order to draw the ray diagram for this condition, first of all we draw a principal axis.

01:08 Here this is the principal axis for this convex lens over which we take a point c which serves as the optical center of this convex lens.

01:23 Now we mark the focal length which is given as 10 cm on both the sides of this optical center.

01:32 Here this one gap will represent 1 centimeter hence this is 1, 2, 3, 4, 5, 6, 7, 8, 9, 10.

01:46 So here, this is 10 centimeter up to here, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10.

02:00 And here also, this is 1, 2, 3, 4, 5, 6, 7, 8, 9, 10.

02:06 10 centimeter here also.

02:16 So, this is the first principal focus and this is the second principal focus at these points.

02:27 Now, we can show the distances equal to twice of the focal length also, which will be 20 centimeter on both the sides of the optical center.

02:41 So if this was 10 centimeter up to here, this will be 1240.

02:53 14, 16, 18, 20.

02:59 And similarly here also this is 12, 14, 16, 18 and 20.

03:14 So these are the distances representing twice of focal length to f2 and to f1.

03:23 Now the object has been kept at a distance of 30 cm.

03:28 But before that, we will draw a convex.

03:32 Lens around this optical center.

03:38 Here, this is the given convex lens.

03:46 This may be representing the line passing through its optical center, the midline, the central line of this convex lens.

03:59 Now, we will measure a distance equal to 30 centimeter, which will represent the object distance.

04:07 So this is obviously more than twice of the focal length.

04:10 So the image should be formed between f and 2f and it should be real and diminished in size.

04:18 So let us check.

04:20 So this is 10 up to here.

04:24 This is 20.

04:25 Then this is 22, 24, 26, 28 and finally this is 30 here.

04:32 So the object can be put at this point.

04:36 It should be exactly perpendicular to the optical center.

04:46 This is the object a, b.

04:51 Now, in order to draw the ray tracing, we take one of the ray traveling parallel to the principal axis.

05:05 So this is one of the ray starting from this object, traveling parallel to the principal axis, which will assume to be moving straight, up to the mid of this convex lens after which it will pass through the principal focus, the first principal focus of this convex lens.

05:34 So we join it here.

05:41 Now we take another ray.

05:44 This was the first ray, which was traveling parallel to the principal axis.

05:47 Now the another ray, it will pass through the optical center.

05:51 So it will pass undeviated like this.

05:57 Now these two rays are meeting at a point here.

06:04 So the image formed will be at this point.

06:12 This is a dash, b dash.

06:16 So if we try to measure the distance of image from the optical center, it comes out to be 2, 4, 6, 8, 10, 12, 13 and approximately 14 cm will be the image distance...

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