Department of Pre-University Education, KarnatakaPUC Karnataka Science Class 12

# Light from a Point Source Falls on a Screen. If the Separation Between the Source and the Screen is Increased by 1%, the Illuminance Will Decrease (Nearly) by - Physics

MCQ
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Light from a point source falls on a screen. If the separation between the source and the screen is increased by 1%, the illuminance will decrease (nearly) by ____________ .

• 0.5%

• 1%

• 2%

• 4%

#### Solution

2%

​Illuminance is  given by

$E = \frac{I_o \cos\theta}{r^2}$

$\theta = 0^0$

$\frac{\Delta r}{r} = 1 \%$

$E = \frac{I_o}{r^2}$

Differentiating,

$dE = - 2\frac{I_o}{r^3}dr$

As approximation differentials are replaced by $\Delta,$

$\Delta E = - 2\frac{I_o}{r^3}\Delta r$

$\Rightarrow \Delta E = - 2\frac{I_o}{r^2}\left( \frac{\Delta r}{r} \right)$

$\Rightarrow \Delta E = - 2E\left( \frac{\Delta r}{r} \right)$

$\Rightarrow \frac{\Delta E}{E} = - 2\left( \frac{\Delta r}{r} \right)$

$\Rightarrow \frac{\Delta E}{E} = - 2 \times 1 \% = - 2 \%$

Since, negative sign implies decrease; hence, illuminance decreases by 2% .\]

Concept: Light Process and Photometry
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#### APPEARS IN

HC Verma Class 11, Class 12 Concepts of Physics Vol. 1
Chapter 22 Photometry
MCQ | Q 5 | Page 454
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