NEET-XII-Physics
22: Photometry
- #9A photographic plate is placed directly in front of a small diffused source in the shape of a circular disc. It takes 12 s to get a good exposure. If the source is rotated by 60° about one of its diameter, the time needed to get the same exposure will be
(a) 6 s
(b) 12 s
(c) 24 s
(d) 48 sdigAnsr: CAns : Correct option
(c)
`` \,\mathrm{\,Here\,},``
`` {t}_{1}=12\,\mathrm{\,s\,}``
`` {\,\mathrm{\,\theta \,}}_{1}={0}^{0}``
`` {\,\mathrm{\,\theta \,}}_{2}={60}^{0}``
`` {\,\mathrm{\,t\,}}_{2}=?``
`` L\,\mathrm{\,et\,}the\,\mathrm{\,distance\,}ber.``
`` L\,\mathrm{\,et\,}the\,\mathrm{\,incident\,}\,\mathrm{\,luminosity\,}be{E}_{o}.``
`` \,\mathrm{\,We\,}\,\mathrm{\,have\,},``
`` {E}_{\theta 1}=\frac{{E}_{o}{\,\mathrm{\,cos\theta \,}}_{1}}{{r}^{2}}``
`` {t}_{1}\alpha \frac{1}{{E}_{\theta 1}}``
`` \Rightarrow {t}_{1}=\frac{{r}^{2}k}{{E}_{o}{\,\mathrm{\,cos\theta \,}}_{1}}``
`` \Rightarrow 12=\frac{{r}^{2}k}{{E}_{o}\,\mathrm{\,cos\,}0}``
`` \Rightarrow \frac{{r}^{2}k}{{E}_{o}}=12``
`` ``
`` S\,\mathrm{\,imilarly\,},``
`` {\,\mathrm{\,t\,}}_{2}=\frac{{\,\mathrm{\,r\,}}^{2}\,\mathrm{\,k\,}}{{\,\mathrm{\,E\,}}_{\,\mathrm{\,o\,}}{\,\mathrm{\,cos\theta \,}}_{2}}=\frac{12}{\,\mathrm{\,cos\,}\left({60}^{0}\right)}``
`` \Rightarrow {\,\mathrm{\,t\,}}_{2}=12\times 2=24\,\mathrm{\,s\,}``
`` ``
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