A spherical lightbulb of diameter 3.548 cm radiates light equally in all directi

Question

A spherical lightbulb of diameter 3.548 cm radiates light equally in all directions, with power 4.602 W.

(a) Find the light intensity at the surface of the lightbulb.
kW/m2

(b) Find the light intensity 7.05 m away from the center of the lightbulb.
mW/m2

(c) At this 7.05-m distance, a lens is set up with its axis pointing toward the lightbulb. The lens has a circular face with a diameter of 14.5 cm and has a focal length of 36.0 cm. Find the diameter of the lightbulb's image.
cm

(d) Find the light intensity at the image.
W/m2

Explanation / Answer

R = 0.03548 / 2 =0.01774

I = P/A

a)

I =  4.602 / ( 4pi* 0.01774^2) =1163.6691

b)

I= 4.602 / ( 4pi* 7.05^2) =0.00736815098

c)

1/v-1/u = 1/f

1/v -1/ -7.05 = 1/ 0.36

v= 0.379372

m = v/u = 0.379372 / 7.05 = 0.0538116312

diameter = 3.548 * 0.0538116312 =0.19092 cm

d)

I = 4.602 / ( 4pi *(7.05 +0.379372 )^2 )

= 0.006634

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