Q94 / 180 · AIIMS 2007 · Physics

A point source is kept at a distance of \(1000 \mathrm{~m}\) has an illumination \(I\). To change the illumination to \(16 I\) the new distance should become

  • Correct answer
    A
    \(250 \mathrm{~m}\)
  • B
    \(500 \mathrm{~m}\)
  • C
    \(750 \mathrm{~m}\)
  • D
    \(800 \mathrm{~m}\)

Solution

For a point source, illuminance at a distance \(r\) is given by Illuminance \(I=\frac{\text { luminous flux } \times \phi}{4 \pi r^2}\) \(\begin{aligned} & \therefore \quad \frac{I}{I^{\prime}}=\left(\frac{r^{\prime}}{r}\right)^2 \\ & \frac{I}{16 I}=\frac{r^{\prime 2}}{(1000 \mathrm{~m})^2} \\ & \text { or } r^{\prime 2}=\frac{(1000 \mathrm{~m})^2}{16} \text { or } r^{\prime}=\frac{(1000 \mathrm{~m})}{4} \\ & r^{\prime}=250 \mathrm{~m} \\ & \end{aligned}\)

Hence, the correct answer is option: 'A'.

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