Question

A helium-neon laser $(\lambda =633\mathrm{nm})$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 ${\theta }_1$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 $1.0\mathrm{km}$?

Short answer

(a) Can a laser beam be perfectly parallel, No

(b) The divergence angle of this laser beam ${0.044}^{\circ }$

(c) The diameter of the laser beam after it travels 3.0m is $4.6\mathrm{mm}$

(d) The diameter of the laser beam after it travels 1.0km is$1.5\mathrm{m}$

Step-by-step solution

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

${\theta }_1=\frac{1\times 22\lambda }{D}$

$$\begin{gathered} {\theta }_1=\frac{1.22\times 6.33\times {10}^{-7}}{1\times {10}^{-3}} \\ =7.73\times {10}^{-4} \\ \mathrm{rad}={0.044}^{\circ } \end{gathered}$$

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,

$\mathrm{\Phi }=2\frac{1.22\times \lambda L}{D}$

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

${\mathrm{\Phi }}_3=2\times \frac{1.22\times 6.33\times {10}^{-7}\cdot 3}{1\times {10}^{-3}}=4.6\mathrm{mm}$

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

${\mathrm{\Phi }}_{km}=2\times \frac{1.22\times 6.33\cdot {10}^{-7}\times 1000}{1\times {10}^{-3}}=1.5\mathrm{m}$