Luminous flux from a point source on the ceiling

[Amith2006]

Please help me with this problem.
# An isotropic point source of 100 candela is fastened to the ceiling of a room. What is the total luminous flux falling on all the walls and floor?
I solved it in the following way:
Here Luminous intensity(I) = 100 cd, Total solid angle(w) = 2 (pi) steradian
Total luminous flux falling on all the walls and floor = I x w
= 100 x 2(pi)
= 100 x 2 x 3.14
= 628 lumens
Is it right?

 

[Andrew Mason]

Please help me with this problem.
# An isotropic point source of 100 candela is fastened to the ceiling of a room. What is the total luminous flux falling on all the walls and floor?
I solved it in the following way:
Here Luminous intensity(I) = 100 cd, Total solid angle(w) = 2 (pi) steradian
Total luminous flux falling on all the walls and floor = I x w
= 100 x 2(pi)
= 100 x 2 x 3.14
= 628 lumens
Is it right?

The walls and floor subtend a solid angle of $\pi$, not $2\pi$.

AM

 

[Amith2006]

The walls and floor subtend a solid angle of $\pi$, not $2\pi$.

AM

I thought the walls and the floor subtended a hemispherical solid angle at the ceiling. Could you please explain how the solid angle is (pi)?

 

[Hootenanny]

I thought the walls and the floor subtended a hemispherical solid angle at the ceiling. Could you please explain how the solid angle is (pi)?

How many radians in half a circle?

 

[Amith2006]

How many radians in half a circle?

There are (pi) radians in a half circle. But I think there are 4(pi) steradians in a sphere. So there are 2(pi) steradians in a hemisphere.
Solid angle(w) = Area of hemisphere/R^2
= [2(pi)R^2]/R^2
= 2(pi) steradians

I think radian is a 2 dimensional unit whereas steradian is a 3 dimensional unit of angle. I may be wrong.

 

[Andrew Mason]

There are (pi) radians in a half circle. But I think there are 4(pi) steradians in a sphere. So there are 2(pi) steradians in a hemisphere.
Solid angle(w) = Area of hemisphere/R^2
= [2(pi)R^2]/R^2
= 2(pi) steradians

I think radian is a 2 dimensional unit whereas steradian is a 3 dimensional unit of angle. I may be wrong.

No. You are right. A sphere subtends $4\pi$ steridians, so the hemisphere is $2\pi$. Sorry about confusing you.

AM

 

[Amith2006]

That's ok. Thanks.