A cub scout makes a simple microscope by placing two...

A cub scout makes a simple microscope by placing two converging lenses of $+18 \mathrm{D}$ at opposite ends of a 28 $\mathrm{cm}$ -long tube. (a) What is the tube length of the microscope? (b) What is the angular magnification? (c) How far should an object be placed from the objective lens?

Key Concepts

Object Distance Relative to Objective Lens

The distance at which an object is placed from the objective lens is critical for ensuring that the real, intermediate image is formed at the correct position for further magnification by the eyepiece. Calculations often involve the thin lens formula and knowledge of the microscope’s tube length and lens focal lengths to achieve the desired image quality and ultimate magnification.

Angular Magnification

Angular magnification describes how much larger an instrument appears to an observer, comparing the angle subtended by the image to that by the object when viewed with the naked eye. In microscopes, it is often determined by multiplying the magnifications provided by the objective and the eyepiece. This concept is fundamental in evaluating the performance of optical instruments.

Thin Lens Equation

The thin lens equation (1/f = 1/d_o + 1/d_i) relates the object distance (d_o), the image distance (d_i), and the focal length (f) of a lens. It is an essential tool in optical calculations, enabling the determination of image position and size given specific lens parameters.

Compound Microscope

A compound microscope uses two or more lenses to produce a magnified image of a small object. The first lens (the objective) forms a real, enlarged image of the object, and the second lens (the eyepiece) acts as a magnifier, producing a further enlarged, virtual image. Understanding the function and interplay of the lenses is crucial to analyzing microscope performance.

Tube Length

Tube length in a compound microscope refers to the distance between the objective and the eyepiece. It is important because it helps determine the positions where the intermediate images are formed and consequently affects the overall magnification and focusing conditions of the instrument.

Lens Power and Focal Length

Lens power is a measure of a lens’s ability to converge or diverge light and is given in diopters (D). The focal length of a lens is the distance over which initially collimated rays are brought to a focus, and it is related to the power by the reciprocal relation, f = 1/P. This relationship is key in designing optical instruments like microscopes.

Transcript

00:01 All right, in this video, we're going to take a look at creating a microscope.

00:05 Okay, so we have two converging lenses.

00:14 Each has a power of 18 diopters.

00:19 Okay, focal length is one over power.

00:23 And so the focal length is one over the 18 diopters.

00:28 This gives us a focal length of 5 .6 times 10 to the minus 2 meters.

00:35 So that's 5 .6 centimeters.

00:40 All right.

00:42 We're using one lens for the objective, one lens for the eye piece.

00:47 So the focal length of the objective equals the focal length of the eyepiece equals 5 .6 centimeters.

00:55 Okay.

00:56 These two converging lenses are at opposite ends of a 28 centimeter two.

01:03 Okay.

01:04 So the lens distance is 28 centimeters.

01:15 All right.

01:16 We need to find the tube length l of the microscope and that is the distance between the focal lengths.

01:25 So tube length l of microscope.

01:33 It is the distance between the focal lengths.

01:35 So what we can say is that the lens distance is equal to the focal length of the eye piece plus the length of the microscope tube plus the length of the objective focal length.

01:56 Okay, solve this for l.

01:58 We get lens distance minus fe minus fo.

02:07 So l is going to be 28 centimeters minus 5 .4.

02:13 0 .6 centimeters minus 5 .6 centimeters...

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