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A helium-neon laser $(\mathrm{λ}=633\mathrm{nm})$is built with a glass tube of inside diameter $1.0\mathrm{mm}$, as shown in FIGURE P33.62. One mirror is partially transmitting to allow the laser beam out. An electrical discharge in the tube causes it to glow like a neon light. From an optical perspective, the laser beam is a light wave that diffracts out through a $1.0$-mm-diameter circular opening.

a. Can a laser beam be perfectly parallel, with no spreading? Why or why not?

b. The angle ${\mathrm{θ}}_1$to the first minimum is called the divergence angle of a laser beam. What is the divergence angle of this laser beam?

c. What is the diameter (in mm) of the laser beam after it travels$3.0\mathrm{m}?$

d. What is the diameter of the laser beam after it travels $1.0\mathrm{km}$?

Step by step solution

01

Diffraction and Angle (part a and b)

a) No, cause turbulence will occur to the portal's aperture.

b) The direction of diverging will be computed by

${\mathrm{θ}}_1=\frac{1×22\mathrm{λ}}{D}$

$$\begin{gathered} {\mathrm{θ}}_1=\frac{1.22×6.33×{10}^{−7}}{1×{10}^{−3}} \\ =7.73×{10}^{−4} \\ \mathrm{rad}={0.044}^{∘} \end{gathered}$$

02

Beam and Position (part c and d)

c and d) The shield's size will just be twice as large as its first darkish fringe's point. It is to add,

$\mathrm{Φ}=2\frac{1.22×\mathrm{λ}L}{D}$

Here get a remedy for the situation at which panel is 3 m away

${\mathrm{Φ}}_3=2×\frac{1.22×6.33×{10}^{−7}â‹\dots 3}{1×{10}^{−3}}=4.6\mathrm{mm}$

Here get a remedy for the situation at which panel is 1km away

${\mathrm{Φ}}_{km}=2×\frac{1.22×6.33â‹\dots {10}^{−7}×1000}{1×{10}^{−3}}=1.5\mathrm{m}$

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