A letter on a page of the compact edition of the O x ford...

A letter on a page of the compact edition of the $O x$ ford English Dictionary is $0.60 \mathrm{~mm}$ tall. A magnifying glass (a single thin lens) held $4.5 \mathrm{~cm}$ above the page forms an image of the letter that is $2.4 \mathrm{~cm}$ tall. (a) Is the image real or virtual? (b) Where is the image? (c) What is the focal length of the lens? Is it converging or diverging?

Key Concepts

Thin Lens Equation

This equation, given by 1/f = 1/do + 1/di, is fundamental in geometrical optics for relating the object distance (do), the image distance (di), and the focal length (f) of a lens. It is used to determine the position and nature (real or virtual) of the image formed by the lens based on an object's position relative to the lens.

Real vs Virtual Images

Understanding the distinction between real and virtual images is crucial in optics. A real image is formed when light rays converge at a point and can be projected onto a screen, while a virtual image is formed when light rays diverge, appearing to originate from a point behind the lens. The determination depends on the geometry of the system and the object’s location with respect to the focal point.

Magnification

Magnification in optics, defined as the ratio of the image size to the object size (and alternatively as -di/do for linear magnification), is a key concept that indicates how much larger or smaller the image appears compared to the object. It provides insight into the image properties and assists in solving for unknown parameters in lens systems.

Converging vs Diverging Lenses

This concept distinguishes between lenses based on their ability to either converge (bring together) or diverge (spread out) light rays. A converging lens has a positive focal length and can produce real images when the object is placed outside the focal point; a diverging lens has a negative focal length and typically forms virtual images. The type of lens is determined by its shape and optical properties, and is fundamental in predicting the behavior of light as it passes through the lens.

Transcript

00:01 A magnifier lens is a lens with a positive focal length, in other words, a converging lens.

00:10 In order to see a magnified, upright image, you typically put the object right inside the focal length.

00:20 In this case, we know the height of our object is a small piece of writing.

00:27 That's 0 .6 millimeters in height.

00:29 And the magnifier produces an image that appears to be quite larger, the height of the image being 24 millimeters.

00:46 We also know how far the object is placed from the lens.

00:52 It is 4 .5 centimeters or 45 millimeters from the lens.

01:01 Okay, and that is the p, which is the object distance.

01:06 So 45 millimeters, putting things all in the same set of units here.

01:15 With imaging, there are two equations that you use.

01:20 One is the thin lens equation, 1 over p, plus 1 over q, the image distance.

01:30 From the lens, those add together to give you 1 over f, the focal length of the lens.

01:36 The other equation that you use is the magnification, which is the height of the image over the object.

01:47 And here we are assuming that the image is going to be upright.

01:51 It's typically what you want to do with writing is to see it upright.

01:56 It is also equal to minus q over p.

02:03 So we have enough information in this case that we can find the magnification...

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