Q12 of 20 Page 287

About 5% of the power of a 100 W light bulb is converted to visible radiation. What is the average intensity of visible radiation

(a) at a distance of 1m from the bulb?


(b) at a distance of 10 m?


Assume that the radiation is emitted isotropically and neglect reflection.

(a) Given : Power of the bulb = 100 W

Since, 5% of the power of a 100 W light bulb is converted to visible radiation, therefore the power of visible radiation can be calculated as follows:



P’ = 5W


The average intensity of visible radiation at a distance of 1m from the bulb can be calculated by using the following formula:



⇒


⇒


⇒ I = 0.398 W/m2


(b) The average intensity of visible radiation at a distance of 10 m from the bulb can be calculated by using the following formula:


I = P’/4π d2


I =


I = 5/1256


I = 0.00398 W/m2


More from this chapter

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10

In a plane electromagnetic wave, the electric field oscillates sinusoidally at a frequency of 2.0 × 1010 Hz and amplitude 48 V m–1.

(a) What is the wavelength of the wave?


(b) What is the amplitude of the oscillating magnetic field?


(c) Show that the average energy density of the E field equals the average energy density of the B field. [c = 3 × 108 m s–1.]

 11

Suppose that the electric field part of an electromagnetic wave in vacuum is

(a) What is the direction of propagation?


(b) What is the wavelength λ?


(c) What is the frequency ν?


(d) What is the amplitude of the magnetic field part of the wave?


(a) Write an expression for the magnetic field part of the wave.

 13

Use the formula λmT = 0.29 cm K to obtain the characteristic temperature ranges for different parts of the electromagnetic spectrum. What do the numbers that you obtain tell you?

 14

Given below are some famous numbers associated with electromagnetic radiations in different contexts in physics. State the part of the electromagnetic spectrum to which each belongs.

(a) 21 cm (wavelength emitted by atomic hydrogen in interstellar space).


(b) 1057 MHz (frequency of radiation arising from two close energy levels in hydrogen; known as Lamb shift).


(c) 2.7 K [temperature associated with the isotropic radiation filling all space-thought to be a relic of the ‘big-bang’ origin of the universe].


(d) 5890 Å - 5896 Å [double lines of sodium]


(e) 14.4 keV [energy of a particular transition in 57Fe nucleus associated with a famous high resolution spectroscopic method (Mössbauer spectroscopy)].