Question

A $100\text{W}$ light bulb is placed at the centre of a spherical chamber of radius $20\text{cm}.$ Assume that $60\%$ of the energy supplied to the bulb is converted into light and the surface of the chamber is partially reflecting. Find the absorption coefficient of the chamber, if pressure exerted by the light on the surface of the chamber is $4.4\times {10}^{-7}{\text{N/m}}^2$.

• A. $0.2$
• B. $0.1$
• C. $0.8$
• D. $0.9$

Answer 1

The correct option is D $0.9$

Given,
$\text{Power}=100\text{W}$
$\text{Radius}=20\text{cm}$
$P_{light}=4.4\times {10}^{-7}{\text{N/m}}^2$

$60\%$ is converted to light, so
$\text{Power supplied to the bulb}\left(P\right)=60\%\text{of}100=60\text{W}$

Now, $\frac{\text{Intensity}}{\text{velocity}}=\frac{P}{\text{area}\times \text{velocity}}$

$\frac{I}{c}=\frac{60}{(4\times 3.14\times {0.2}^2)\times (3\times {10}^8)}$

$\frac{I}{c}=4\times {10}^{-7}{\text{N/m}}^2$.

Pressure exerted by light $\left(P_{light}\right),$

$P_{light}=\frac{I}{c}(1+r)=4.4\times {10}^{-7}$

$\Rightarrow 1+r=1.1\Rightarrow r=0.1$

$\therefore$ absorption coefficient $\alpha =1-r=1-0.1=0.9$

Hence, $\left(\text{D}\right)$ is the correct answer.