Infrared and terahertz studies of polar phonons and magnetodielectric effect in multiferroic<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi mathvariant="normal">Bi</mml:mi><mml:mi mathvariant="normal">Fe</mml:mi><mml:msub><mml:mi mathvariant="normal">O</mml:mi><mml:mn>3</mml:mn></mml:msub></mml:mrow></mml:math>ceramics

$\mathrm{Bi}\mathrm{Fe}{\mathrm{O}}_{3}$ ceramics were investigated by means of infrared reflectivity and time domain terahertz transmission spectroscopy at temperatures $20--950\phantom{\rule{0.3em}{0ex}}\mathrm{K}$, and the magnetodielectric effect was studied at $10--300\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ with the magnetic field up to $9\phantom{\rule{0.3em}{0ex}}\mathrm{T}$. Below $175\phantom{\rule{0.3em}{0ex}}\mathrm{K}$, the sum of polar phonon contributions to the permittivity corresponds to the value of measured permittivity below $1\phantom{\rule{0.3em}{0ex}}\mathrm{MHz}$. At higher temperatures, a giant low-frequency permittivity was observed, obviously due to the enhanced conductivity and possible Maxwell-Wagner contribution. Above $200\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ the observed magnetodielectric effect is caused essentially through the combination of magnetoresistance and the Maxwell-Wagner effect, as recently predicted by Catalan [Appl. Phys. Lett. 88, 102902 (2006)]. Since the magnetodielectric effect does not occur due to a coupling of polarization and magnetization as expected in magnetoferroelectrics, we call it an improper magnetodielectric effect. Below $175\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ the magnetodielectric effect is by several orders of magnitude lower due to the decreased conductivity. Several phonons exhibit gradual softening with increasing temperature, which explains the previously observed high-frequency permittivity increase on heating. The observed noncomplete phonon softening seems to be the consequence of the first-order nature of the ferroelectric transition.