Past exam of the short options paper shared by Prelims and Parts A and B of the physics course of the University of Oxford / 2018 / S2 / 1 / a / Solution

The distance modulus at $100\mathrm{pc}$ is five magnitudes. Thus the two approximate main-sequence endpoints read from the original figure, $m_V\simeq 0,20$, correspond to $M_V\simeq -5,15$. With the given solar reference,Use the figure's approximate endpoint effective temperatures $25,000$ K and $2500$ K. If $V$-band luminosity is used as a rough bolometric proxy, the Stefan–Boltzmann law givesTaking $T_{\odot }\simeq 5800$ K givesThese are schematic estimates, not precision radii. The diagram supplies $V$ magnitudes rather than bolometric luminosities, and hot and cool endpoints need different bolometric corrections. The exact range cannot be recovered without those corrections; the quoted values state the intended approximation explicitly.