CBSE-XI-Physics
22: Photometry
- #8A photographic plate placed a distance of 5 cm from a weak point source is exposed for 3 s. If the plate is kept at a distance of 10 cm from the source, the time needed for the same exposure is
(a) 3 s
(b) 12 s
(c) 24 s
(d) 48 sdigAnsr: CAns : Correct option
(b)
Here,
`` {d}_{1}=5cm=0.05\,\mathrm{\,m\,}``
`` {d}_{2}=10cm=0.1\,\mathrm{\,m\,}``
`` {t}_{1}=3s``
`` {t}_{2}=?``
`` \,\mathrm{\,Suppose\,}the\,\mathrm{\,actual\,}\,\mathrm{\,incident\,}\,\mathrm{\,illuminance\,}be{E}_{o}``
`` \,\mathrm{\,Suppose\,}the\,\mathrm{\,iluminance\,}at3\,\mathrm{\,cm\,}\,\mathrm{\,distance\,}be{E}_{d1}``
`` \,\mathrm{\,Suppose\,}the\,\mathrm{\,iluminance\,}at10\,\mathrm{\,cm\,}\,\mathrm{\,distance\,}be{E}_{d2}``
`` \,\mathrm{\,cos\,}\theta =1``
`` {E}_{d1}=\frac{{E}_{o}}{{{d}_{1}}^{2}}``
`` \,\mathrm{\,Now\,},``
`` {\,\mathrm{\,t\,}}_{1}\,\mathrm{\,\alpha \,}\frac{1}{{\,\mathrm{\,E\,}}_{\,\mathrm{\,d\,}1}}``
`` \Rightarrow {\,\mathrm{\,t\,}}_{1}=\frac{\,\mathrm{\,k\,}}{{\,\mathrm{\,E\,}}_{\,\mathrm{\,d\,}1}}``
`` \Rightarrow {\,\mathrm{\,t\,}}_{1}=\frac{\,\mathrm{\,k\,}{5}^{2}}{{\,\mathrm{\,E\,}}_{\,\mathrm{\,o\,}}}``
`` \Rightarrow \frac{\,\mathrm{\,k\,}}{{\,\mathrm{\,E\,}}_{\,\mathrm{\,o\,}}}=\frac{3}{25}``
`` S\,\mathrm{\,imilarly\,},``
`` \Rightarrow {\,\mathrm{\,t\,}}_{2}=\frac{\,\mathrm{\,k\,}{10}^{2}}{{\,\mathrm{\,E\,}}_{\,\mathrm{\,o\,}}}``
`` \Rightarrow {\,\mathrm{\,t\,}}_{2}=\frac{3}{25}\times {10}^{2}=12\,\mathrm{\,s\,}``
`` ``
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