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Chapter 35: Q . 43 (page 1019)

High-power lasers are used to cut and weld materials by focusing the laser beam to a very small spot. This is like using a magnifying lens to focus the sun’s light to a small spot that can burn things. As an engineer, you have designed a laser cutting device in which the material to be cut is placed 5.0 cm behind the lens. You have selected a high-power laser with a wavelength of 1.06 mm. Your calculations indicate that the laser must be focused to a 5.0@mm@diameter spot in order to have sufficient power to make the cut. What is the minimum diameter of the lens you must install?

Short Answer

Expert verified

This is like using a magnifying lens to focus the sun’s light to a small spot that can burn things

Step by step solution

01

Given Information

This is like using a magnifying lens to focus the sun’s light to a small spot that can burn things

02

 Step 2 : Calculation

The laser must be focused to a 5.0@mm@diameter spot in order to have sufficient power to make the cut

03

simplify

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Most popular questions from this chapter

The resolution of a digital camera is limited by two factors:

diffraction by the lens, a limit of any optical system, and the fact

that the sensor is divided into discrete pixels. Consider a typical

point-and-shoot camera that has a 20-mm-focal-length lens and

a sensor with 2.5@mm@wide pixels.

a. First,ass ume an ideal, diffractionless lens. At a distance of

100 m, what is the smallest distance, in cm, between two

point sources of light that the camera can barely resolve? In

answering this question, consider what has to happen on the

sensor to show two image points rather than one. You can use

s′ = f because s W f.

b. You can achieve the pixel-limited resolution of part a only if

the diffraction width of each image point is no greater than

1 pixel in diameter. For what lens diameter is the minimum

spot size equal to the width of a pixel? Use 600 nm for the

wavelength of light.

c. What is the f-number of the lens for the diameter you found in

part b? Your answer is a quite realistic value of the f-number

at which a camera transitions from being pixel limited to

being diffraction limited. For f-numbers smaller than this

(larger-diameter apertures), the resolution is limited by the

pixel size and does not change as you change the aperture. For

f-numbers larger than this (smaller-diameter apertures), the

resolution is limited by diffraction, and it gets worse as you

“stop down” to smaller apertures

Two converging lenses with focal lengths of 40cmand 20cmare 10cmapart. A 2.0cmtall object is 15cmin front of the40cmfocal-length lens.

a. Use ray tracing to find the position and height of the image. Do this accurately using a ruler or paper with a grid, then make measurements on your diagram.

b. Calculate the image position and height. Compare with your ray-tracing answers in part a.

Two light bulbs are 1.0mapart. from, what distance can these light bulbs be marginally resolved by a small telescope with a 4.0-cm-diameterobjective lens? assume that the lens is diffraction limited andλ=600nm.

A hydrogen discharge lamp emits light with two prominent wavelengths: 656nm(red) and 486nm(blue). The light enters

a flint-glass prism perpendicular to one face and then refracts

through the hypotenuse back into the air. The angle between

these two faces is 35°.

a. Use Figure 35.18to estimate to ±0.002the index of refraction

of flint glass at these two wavelengths.

b. What is the angle (in degrees) between the red and blue light

as it leaves the prism?

Modern microscopes are more likely to use a camera than human viewing. This is accomplished by replacing the eyepiece in Figure 35.14 with a photo-ocular that focuses the image of the objective to a real image on the sensor of a digital camera. A typical sensor is 22.5 mm wide and consists of 5625 4.0@mm@ wide pixels. Suppose a microscopist pairs a 40* objective with a 2.5* photo-ocular.

a. What is the field of view? That is, what width on the microscope stage, in mm, fills the sensor?

b. The photo of a cell is 120 pixels in diameter. What is the cell’s actual diameter, in mm?
See all solutions

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