How to obtain impulse response from a plot of magnitude of frequency response?
You state in your question that you have a "magnitude response". In that case, you cannot reconstruct the time-domain signal corresponding to the impulse response, because phase information is missing. In the plot, however, the vertical axis is indexed by $H(e^{j\omega})$ and not $|H(e^{j\omega})|$, so I suppose you meant "frequency response".

You can relate a system's frequency response to its respective impulse response via inverse DTFT:

$$H(e^{j\omega}) \xrightarrow{\mathscr{F^{-1}}} h(n)$$

Note that you have a typical ideal low-pass filter. That has a well-known DTFT inverse.