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

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MCQ
Fill in the Blanks

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 ____________ .

Options

  • 0.5%

  • 1%

  • 2%

  • 4%

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Solution

2%

 

‚ÄčIlluminance 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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