Unit solid angle and finite angle

[lkijmj]

Homework Statement

A point source emits visible light isotropically. Its luminous flux is 0.11 lumen. Find the flux whithin the cone that has half angle of 30 degree from the light source.

Homework Equations

luminous flux = luminous intensity * solid anlge

The Attempt at a Solution

I tried to divide the flux 0.11lumen by 4pi and then multiply the solid angle. But since the solid angle of the cone is 0.84sr, the result appears to be smaller than the luminous intensity. But I don't understand the result. Can the flux of finite solid angle be smaller than luminous intensity?

 

[gneill]

Luminous flux is the total perceived power emitted in all directions (4pi steradians).
Luminous intensity is the perceived power per unit solid angle.

So you divided the given luminous flux by 4pi steradians in order to obtain the luminous intensity, and then multiplied by the given solid angle in order to find the flux within that solid angle. Looks okay to me.

 

[lkijmj]

But it doesn't make sense that luminous flux is smaller than luminous intensity. How can I explain this?

 

[gneill]

But it doesn't make sense that luminous flux is smaller than luminous intensity. How can I explain this?

The intensity is the perceived luminous power per unit solid angle (i.e. per steradian).

You found the solid angle of interest to be 0.842 sr. That's less than one steradian. So naturally the resulting flux will be less than the flux for a whole steradian.