Asked by SABRINA

A POINT SOURCE OF LIGHT IS PLACED 50 CM ABOVE A CIRCULAR CARD OF DIAMETER 5CM, THE SOURCE BEING DIRECTLY ABOVE THE CENTRE OF THE CARD. WHAT IS THE AREA OF THE SHADOW ON THE FLOOR 70 CM BELOW THE CARD?
Answered by drwls
The diameter of the shadow is D = 5 cm immediately below the circular card. At distances farther below the card, the diameter of the shadow grows in proportion to the distance from the point source.

70 cm below the card is 120 cm from the point source. The diameter of the shadow there is (120/50)*5 = 12 cm

The area of the shadow there would be
(pi/4)*12^2 = 36 pi = 113.1 cm^2
Answered by SABRINA
THANK YOU!
Answered by SABRINA
WHAT DOES PI STAND FOR?
Answered by Damon
Sabrina,
pi is an irrational number approximated by 3.14159
It is the ratio of the circumference of a circle to the diameter.
C = pi D
the area of the circle is ten
A = pi R^2 = pi (D^2)/4
Answered by Damon
the area of the circle is then
A = pi R^2 = pi (D^2)/4
Answered by drwls
pi = 3.141592...
It is the ratio of the circumference to the radius of a circle.
It is usually represented by a Greek letter, but I cannot type it here.
Answered by SABRINA
thank you
would what the nature of the shadow be if the point of source of light is replaced by a luminous disc of diameter 5 cm, whose centre lies directly above the centre of the card?
Answered by Damon
pe·num·bra/peˈnəmbrə/
Noun:

The partially shaded outer region of the shadow cast by an opaque object.

The shadow cast by the earth or moon over an area experiencing a partial eclipse.
Answered by SABRINA
thank you
what would the dimension of shadow be?
Answered by Damon
directly below the card, dark

after you get out from that complete shadow, you can look up and see part of the light so you are in partial shadow until you get far enough out to see the entire light.
Answered by Damon
Now when will you see the entire light above?
Geometry
from left point on light, 2.5 cm to left of center, through right side of card, 2.5 cm right of center 50 cm down
A is angle of ray from vertical
tan A = 5/50
now the same angle down from the right side of the card
tan A = 5/50 = x/70
x = 5 (70/50)
x is to the right of thge complete shadow so distance from center to that point is
2.5 + 5(70/50)
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