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

Correct answer: A. (250 ~m) For a point source, illuminance at a distance r is given by Illuminance (I= luminous flux × φ 4 π r^2 ) aligned & I I^ =( r^ r )^2 & (I)/(16 I)= r^ 2 (1000 m)^2 & or r^ 2 = (1000 m)^2 16 or r^ = (1000 m) 4 & r^ =250 m & aligned )

AIIMS 2007

Exam: AIIMS
Year: 2007
Subject: Physics
Chapter: Wave Optics

AIIMS 2007 · Physics · Wave Optics

A point source is kept at a distance of (1000 ~m) has an...

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

Options

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

Correct answer

A. (250 \mathrm{~m})

Step-by-step 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{\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}

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