Final answer:
The minimum thickness of the screen for a given decibel attenuation M can be calculated using the formula t = M / (20α log10(e)), where α is the absorption coefficient of the material and t is the thickness of the screen.
Step-by-step explanation:
The student's question concerns the minimum thickness t that an infinite plane screen needs to have to attenuate a uniform plane wave by M decibels (dB), given the absorption coefficient α of the material. To find the minimum thickness for a desired attenuation, we can use the formula for attenuation in decibels given by AdB = 20 log10(Em(z) / Em(z+t)), where Em(z) is the electric field magnitude of the wave at position z and Em(z+t) is the magnitude at position z plus the thickness t. The thickness t is related to the absorption coefficient α and desired decibel attenuation M through the following relationship: t = M / (20α log10(e)), where log10(e) is the natural logarithm of e, the base of the natural logarithms, with respect to base 10.