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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 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 5.0cmbehind the lens. you have selected a high-power laser with a wavelength of

your calculation indicates that the laser must be focused to a 5.0-渭m-diameterspot in order to have sufficient power to make the cut. what is the minimum diameter of lens you must install?

Short Answer

Expert verified

The minimum diameter of the lens is2.58cm.

Step by step solution

01

Given information

We have given that:

High power laser wavelength 位=1.06x10-6m

Laser cutting devicef=5cm鈫�5.0x10-2m

sufficient power to cut laser 蝇=5渭m鈫�5.0x10-6m

we need to find the diameter of lens to install.

02

Simplification

Let us use this formula,

蝇=2.44位fD

Here, fis the focal length, 位is wavelength and 蝇 is the value for laser must be focused.

Now multiplying both sides by D,

localid="1649142735572" D脳蝇=D脳2.44位fD

localid="1649142750541" D脳蝇=2.44位f

Dividing both the sides by 蝇,

D脳蝇蝇=2.44位f蝇

D=2.44位f蝇

Let us substitute values in the equation,

D=2.44(1.06x10-6m)(5.0x10-2m)5.0x10-6m

D=0.0258m鈫�2.58cm.

Here,Dis the diameter of the lens.

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