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Question: The luminous intensity of \(100W\) unidirectional bulb is \(100\text{ candela}\). The total luminous...

The luminous intensity of 100W100W unidirectional bulb is 100 candela100\text{ candela}. The total luminous flux emitted from bulb will be
A. 100π lumen B. 200π lumen C. 300π lumen D. 400π lumen \begin{aligned} & \text{A}\text{. }100\pi \text{ lumen} \\\ & \text{B}\text{. }200\pi \text{ lumen} \\\ & \text{C}\text{. }300\pi \text{ lumen} \\\ & \text{D}\text{. }400\pi \text{ lumen} \\\ \end{aligned}

Explanation

Solution

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 4π4\pi .

Formula used:
Luminous flux=Luminous intensity×solid angle\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.
cd = lmsr\text{cd = }\dfrac{\text{lm}}{\text{sr}}
Luminous flux=Luminous intensity×solid angle\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,
Luminous intensity=100W Solid angle=4π \begin{aligned} & \text{Luminous intensity}=100W \\\ & \text{Solid angle}=4\pi \\\ \end{aligned}
(For unidirectional bulb, solid angle is considered as 4π4\pi )
Therefore,
Luminous flux=100×4π=400π \text{Luminous flux}=100\times 4\pi =400\pi \text{ }
The total luminous flux emitted from bulb is 400π lumen400\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.