X-ray Telescope Mirror Design · AI Generator #GEN-5EC3C988

Physics · modern-physics

Problem

The Chandra X-ray Observatory uses grazing incidence mirrors to focus X-rays, since X-rays would be absorbed by conventional mirrors. For efficient reflection at grazing angles, the X-ray photon energy must be below a critical threshold related to the mirror material. Consider an iridium-coated mirror designed to reflect X-rays at a grazing angle of

\theta = 1.2°

from the surface. The critical energy

E_c

for total external reflection occurs when the X-ray's effective refractive index equals unity. For X-rays, this critical energy is given by:

E_c = \frac{hc}{2\pi} \sqrt{\frac{\rho N_A Z}{A} r_e \sin\theta}

where

\rho = 22.6\;\text{g/cm}^3

is iridium's density,

Z = 77

is its atomic number,

A = 193\;\text{g/mol}

is its atomic mass, and

r_e = 2.82 \times 10^{-15}\;\text{m}

is the classical electron radius. A cosmic X-ray source emits photons with energy

E = 8.5\;\text{keV}

. Will these X-rays be efficiently reflected by this mirror design?

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