2. The Laser

1. How much surface roughness must a target screen have in order to see a speckle pattern with a HeNe laser? (Assume that the optical axis of laser beam and visual field of view are normal at he target surface) is the more than one solution for the surface roughness?
2. There are many longitudinal oscillation modes in a resonator having a length $\ell$ , with wavelengths $\lambda =\frac{2\cdot \ell }{n}$ (where $n$ is an integer number).
   We consider a HeNe laser having 30 cm resonator length. Please calculate the frequency difference of of two neighbouring oscillation modes at the HeNe laser emission wavelength.
   We assume a natural linewidth (the ‘uncertainty’ of the laser light frequency) of 2 GHz. What is the consequence for the emitted frequency of the laser? Which role plays the length of the resonator?
3. Snell‘s refraction law $\frac{sin\alpha }{sin\beta }=\frac{n_2}{n_1}$ is well-known. The incidence angle $\alpha$ becomes the Brewster angle ${\alpha }_B$ if the angle between refracted and reflected light beams is 90°. Please derive an equation which describes the dependence of the Brewster angle on the refractive index!
4. We consider a CW laser having 30 cm resonator length. Assuming that 10% of the light falling on the partially reflecting resonator mirror are transmitted, which distance must a photon propagate on average in order to initiate an induced emission?
5. Check out the laser applet at the end of the chapter. Please describe what the applet shows in physically correct terms.
6. Describe in your own words, why thermal light sources do not emit laser light.
7. Investigate in the literature the various laser types and their specific fields of application. Which properties are crucial for the various applications? Justify your results with arguments.
8. Try to identify alternative conventional light sources for the applications which you identified in the previous question. Discuss the pros and cons of lasers and conventional light sources.
9. Laser light can be dangerous! Whaat makes laser light more dangerous to the eye than the light of a tungsten lamp having the same optical power?