ARCHITECTURAL | Specialty | 1 Question (EASY)

ARCHITECTURAL LIGHTING (Beam Angle)

(1 Question, Difficulty Level: EASY)
by Raison John J. Bassig

In the dining area with a 3.20-m ceiling height of the house you designed, you specified a circular hanging downlight centered above the space allocated for a dining table. According to the lamp manufacturer, its beam angle is 52°.

Your client then bought a round dining table, measuring 160cm-diameter x 62cm-high, and instructed you as her architect, that the direct lighting from the lamp should illuminate only up to the exact edge of the table. What will be the resulting mounting height of the hanging lighting fixture measured from the ceiling to accomplish your client's requirement?

(Image courtesy of Bumpermankh.com, modified)

a. About 0.94m from the ceiling
b. About 1.33m from the ceiling
c. About 1.56m from the ceiling
d. About 0.62m from the ceiling

The fixture's mounting height from the ceiling can be determined by,

Mounting Height = [ Ceiling Height ] - [ Table Height ] - [ Height of Fixture from Table ]

But the [ Height of Fixture from Table ] is unknown, so, we must solve this first.

Since the fixture is directly along the centerline of the table, we can divide the light fixture and the table in half (along their centerlines), to produce a right triangle, where we can use a simple trigonometric function (Tangent equation) to solve the unknown. By dividing the components in half, the given beam angle would also be divided in half and will serve as one of the interior angles of the right triangle, while half of the table's surface would now be the opposite side of the triangle, and the [ Height of Fixture from Table ] would be the adjacent side of the triangle,

Recall: Tan(Angle) = Opposite / Adjacent

where:
The Angle is half the given beam angle
The Opposite side is half the length of the table (or, since the table is round, the radius)
The Adjacent side is the [ Height of Fixture from Table ]

So,

Tan( [52°] / 2 ) = ( [1.6m] / 2 ) / [ Height of Fixture from Table ]
Tan(26°) = 0.8m / [ Height of Fixture from Table ]
[ Height of Fixture from Table ] = 0.8m / Tan26°
[ Height of Fixture from Table ] = 1.64m

Now that we know the [ Height of Fixture from Table ], we can solve the fixture's mounting height from the ceiling,

Mounting Height = [ Ceiling Height ] - [ Table Height ] - [ Height of Fixture from Table ]
Mounting Height = [3.20m] - [0.62m] - [1.64m]
Mounting Height = 0.94m

Here's an illustration to better understand the solution:

Therefore, the correct answer is a. About 0.94m from the ceiling.