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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

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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 objective lens of a telescope is a symmetric glass lens with $100 c m$ radii of curvature. The eyepiece lens is also a symmetric glass lens. What are the radii of curvature of the eyepiece lens if the telescope’s magnification is $20 \times$ ?

A $20 x$ telescope has a $12 c m$ diameter objective lens. What minimum diameter must the eyepiece lens have to collect all the light rays from an on-axis distant source?

A beam of white light enters a transparent material. Wavelengths for which the index of refraction is n are refracted at angle u2. Wavelengths for which the index of refraction is n + dn, where dn V n, are refracted at angle u2 + du.

a. Show that the angular separation of the two wavelengths, in radians, is du = -1dn/n2 tan u2.

b. A beam of white light is incident on a piece of glass at 30.0°. Deep violet light is refracted 0.28° more than deep red light. The index of refraction for deep red light is known to be 1.552. What is the index of refraction for deep violet light?

The Hubble Space Telescope has a mirror diameter of 2.4 m. Suppose the telescope is used to photograph stars near the center of our galaxy, 30,000 light years away, using red light with a wavelength of 650 nm.

a. What’s the distance (in km) between two stars that are marginally resolved? The resolution of a reflecting telescope is calculated exactly the same as for a refracting telescope.

b. For comparison, what is this distance as a multiple of the distance of Jupiter from the sun?

The lens shown in FIGURE CP $35.49$ is called an achromatic doublet, meaning that it has no chromatic aberration. The left side is flat, and all other surfaces have radii of curvature R.

a. For parallel light rays coming from the left, show that the effective focal length of this two-lens system is $f = R / 12 n_{2} - n_{1} - 12$ , where localid="1648757054673" $n_{1}$ and $n_{2}$ are, respectively, the indices of refraction of the diverging and the converging lenses. Don’t forget to make the thin-lens approximation.

b. Because of dispersion, either lens alone would focus red rays and blue rays at different points. Define $∆ n_{1}$ and $∆ n_{2}$ as $n_{b l u e} - n_{r e d}$ for the two lenses. What value of the ratio $∆ n_{1} / ∆ n_{2}$ makes $f_{b l u e} = f_{r e d}$ for the two-lens system? That is, the two-lens system does not exhibit chromatic aberration.

c. Indices of refraction for two types of glass are given in the table. To make an achromatic doublet, which glass should you use for the converging lens and which for the diverging lens? Explain

$n_{b l u e}$ $n_{r e d}$

Crown glass 1.525 1.517

Flint glass 1.632 1.616

d. What value of R gives a focal length of $10.0 c m$ ?

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