How far from a page should you hold a lens with 29-cm focal length in order to see the print mag

How far from a page should you hold a lens with 29-cm focal...

Key Concepts

Thin Lens Equation

The thin lens equation relates the focal length of a lens to the distances of the object and the image from the lens using the formula 1/f = 1/do + 1/di. This equation is fundamental in optics as it provides a way to determine one of these distances when the other and the focal length are known.

Magnification

Magnification in optics is defined as the ratio of the image size to the object size, often expressed as m = -di/do for thin lenses. This concept is important for understanding how optical instruments, such as magnifiers, enlarge images and how the image distance relates to the perceived size change.

Virtual Image Formation

Virtual image formation occurs when the light rays diverge after passing through a lens, making the image appear as if it is located on the same side of the lens as the object. This concept is critical in devices like magnifying glasses, where the enlarged view is created by viewing a virtual image that cannot be projected onto a screen.

Transcript

00:01 Okay, problem 45 asks how far should we hold, how far from a page should you hold a lens with a 29 centimeter focal length in order to see the printed, print magnified 2 .2 times.

00:16 So the two pieces of information we're given are the focal length is 29 centimeters, and that's a positive value.

00:25 So we know it's a convex lens and the magnification, which is positive 2 .2.

00:32 So we're going to use two relationships.

00:34 One, the magnification equation, which is the magnification is equal to the ratio of the image distance over the object distance.

00:45 And then the other one that we'll use is the lens equation, which is one over the focal length is equal to one over s plus one over s prime.

00:54 So we can get this down to two unknowns, and we have two equations, so that will help us solve the problem.

01:01 So if 2 .2 is our magnification, that's equal to negative s prime over s, we can express s prime as negative 2 .2 times s.

01:13 And then we can plug that into our lens equation.

01:17 So i'll write it down here.

01:19 One over focal length, which is 29, and i can leave it in centimeters, is equal to 1 over s plus 1 over negative 2 .2s.

01:30 So now, just getting a common denominator on my right hand side 1 over 29 equals 2 .2 over 2 .2 s minus 1 over 2 .2s.

01:47 Now i have the same denominator.

01:49 2 .2 minus 1 is 1 .2 over 2 .2 s.

01:56 It sort of looks like 2 .25, but 2 .2s is my right hand side.

02:02 Denominator.

02:03 So 1 over 29 is equal to 1 over, i'm sorry, 1 .2 over 2 .2 s...

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