Do there exist any clothing like fabric which could effectively block rays from a cellphone?
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It turns out that you need comparatively little thickness of a conductive material to effectively block the GHz frequencies of mobile phones. The two mechanisms that do this are reflection of the waves and then secondly, absorption of the waves in the conductive material through Ohmic heating.
In answering this question, I arrived at a formula for the power attenuation caused by a sheet of aluminium film.
$$\left[\frac{E_t}{E_i}\right]^2 \simeq \left[4 \frac{\eta_{\rm Al}}{\eta_0} \exp(-t/\delta)\right]^2 \simeq 0.22 \omega^{-1} \exp(-44 \omega^{1/2} t),$$ where $\delta = (2/\mu_r \mu_0 \sigma \omega)^{1/2}$ is the skin depth, $\sigma$ is the conductivity ($3.5\times 10^7$ S/m for Al), $t$ is the foil thickness in metres and $\omega$ is the angular frequency in s$^{-1}$.
So at 1 GHz ($\omega \simeq 6\times 10^{9}$ s$^{-1}$) a sheet of metallised film, coated with aluminium with a thickness of $\sim 10^{-6}$ m, would offer a power attenuation factor of $\sim 10^{-12}$.
That would easily do the job - but there is a caveat. You cannot have holes or tears in the fabric that are even nearly comparable with the wavelength of the radiation (30 cm). Punctures would probably be ok, but you would need to have a way of sealing it up. Note that you could not breathe inside a bag made of this substance!
Other possibilities beside metallised film can be found by looking up conductive textiles. A brief search suggests that you can get these fabrics at reasonable prices. The calculations of their effectiveness will vary with the conductivity and thickness of the material, but should be comparable with the calculations above.
