Question

An electric bulb is hanging over a table at a height of 1 m above it. The illuminance on the table directly below the bulb is 40 lux. The illuminance at a point on the table 1 m away from the first point will be about
(a) 10 lux
(b) 14 lux
(c) 20 lux
(d) 28 lux

Answer 1

(b) 14 lux

Explanation:

r = √2

tan θ = BC / AB = 1.

Please refer attached picture for the diagram.

I(o) = 40 lux

θ = tan⁻¹ (1) = 45°

Formula for illuminance = E = I(o) Cos θ / r²

= 40 * Cos 45° / (√2)²

= (40 * 1/√2) / 2

= 20 / √2

= √2 * 10

= 1.41 * 10

= 14.1 lux

Option B is the answer.

Answer 2

An electric bulb is hanging over a table at a height of 1 m above it. The illuminance on the table directly below the bulb is 40 lux. The illuminance at a point on the table 1 m away from the first point will be about 14 lux.

Explanation:

Given data in the question  :

An electric bulb hangs above a table at an altitude of 1 m above it

The illumination immediately below the bulb on the table is 40 lux.

l.e  

$I_0$  = 40  lux  

Here, r =√ 2

$\tan \theta=\frac{B C}{A B}=\frac{\text { perpendicular }}{\text { base }}=1$

BC is perpendicular  

AB is base  

$\theta=\tan ^{-1}(1)=45^{\circ}$

The illuminance is given by

$E=\frac{I_{0} \cos \theta}{r^{2}}$

$E=\frac{40 \times \cos \left(45^{\circ}\right)}{\sqrt{2}^{2}}$

  $=14 \mathrm{lux}$