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Hint: Luminous intensity is a quantity for characterising a light source. We will find the relation between luminous flux, luminous intensity and the solid angle to determine the value of luminous flux. For a unidirectional bulb, solid angle will be $4\pi $.
Formula used:
$\text{Luminous flux}=\text{Luminous intensity}\times \text{solid angle}$
Complete step by step answer:
Luminous flux or luminous power in photometry is a measure of the perceived power of light. We can say that luminous power is a measure of the total amount of visible light emitted by a lamp. Luminous intensity can be expressed as the rate of transmission of luminous energy. The SI unit of luminous flux is lumen.
Luminous intensity is a measurement of the wavelength-weighted power emitted by a light source in a particular direction per unit solid angle. Luminous intensity is a quantity for characterising a light source. It is described as the luminous flux per unit solid angle. The SI unit of the luminous intensity is the candela, that is, lumen per steradian.
$\text{cd = }\dfrac{\text{lm}}{\text{sr}}$
$\text{Luminous flux}=\text{Luminous intensity}\times \text{solid angle}$
When the luminous angle of a light source is one solid angle and the luminous flux is one lumen, then, its luminous intensity is one candela.
We have,
$\begin{align}
& \text{Luminous intensity}=100W \\
& \text{Solid angle}=4\pi \\
\end{align}$
(For unidirectional bulb, solid angle is considered as $4\pi $)
Therefore,
$\text{Luminous flux}=100\times 4\pi =400\pi \text{ }$
The total luminous flux emitted from bulb is $400\pi \text{ lumen}$
Hence, the correct option is D.
Note:
Luminous flux is the measure of the total perceived power of light while luminous intensity is a measurement of the perceived power emitted by a light source in a particular direction per unit solid angle. Solid angle is the three dimensional (3d) analogue of an angle.
Formula used:
$\text{Luminous flux}=\text{Luminous intensity}\times \text{solid angle}$
Complete step by step answer:
Luminous flux or luminous power in photometry is a measure of the perceived power of light. We can say that luminous power is a measure of the total amount of visible light emitted by a lamp. Luminous intensity can be expressed as the rate of transmission of luminous energy. The SI unit of luminous flux is lumen.
Luminous intensity is a measurement of the wavelength-weighted power emitted by a light source in a particular direction per unit solid angle. Luminous intensity is a quantity for characterising a light source. It is described as the luminous flux per unit solid angle. The SI unit of the luminous intensity is the candela, that is, lumen per steradian.
$\text{cd = }\dfrac{\text{lm}}{\text{sr}}$
$\text{Luminous flux}=\text{Luminous intensity}\times \text{solid angle}$
When the luminous angle of a light source is one solid angle and the luminous flux is one lumen, then, its luminous intensity is one candela.
We have,
$\begin{align}
& \text{Luminous intensity}=100W \\
& \text{Solid angle}=4\pi \\
\end{align}$
(For unidirectional bulb, solid angle is considered as $4\pi $)
Therefore,
$\text{Luminous flux}=100\times 4\pi =400\pi \text{ }$
The total luminous flux emitted from bulb is $400\pi \text{ lumen}$
Hence, the correct option is D.
Note:
Luminous flux is the measure of the total perceived power of light while luminous intensity is a measurement of the perceived power emitted by a light source in a particular direction per unit solid angle. Solid angle is the three dimensional (3d) analogue of an angle.
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