Question

A battery operated torch is adjusted to send an almost parallel beam of light. It produces an illuminance of $40lux$ when light falls on a wall 2m away. The illuminance produced when it falls on a wall 4m away is close to.
A) $40lux$
B) $20lux$
C) $10lux$
D) $5lux$

Answer 1

Hint:Illuminance is defined as the total luminous flux incident on any surface per unit area of the surface. Illuminance is the brightness of the light. Beams of light have rays parallel to each other which mean that the beam of light can travel far distance without loss in power.

Formula used: ${\text{I}} = \dfrac{P}{{\text{A}}}$ where I is the illuminance of the beam of light P is the illuminance power and A is the area of cross section.

Step by step solution:
As it is given that the illuminance of the light is $40lux$ and the beam of light falls on the wall which is 2m away. As the particles of beams of light are parallel to each other which means that the area of the light will remain the same.

Now as the illuminance produced on the wall which is 2m away is $40lux$ and the illuminance is given by,
${\text{I}} = \dfrac{P}{{\text{A}}}$
Where I is the illuminance of the beam of light P is the illuminance power and A is the area of cross section.

We know that the power of the beam of light at 2m away wall is$40lux$. The area of the cross section of the beam of light is constant and the power will also not change as the distance of travelling of the beam of light is very less. So option A is the correct answer for this problem and as the illuminance remains the same.

Note: It is advisable to students to remember the formula of the illuminance as it helps to solve the problems of these kinds and also some of the problems. The power of the beam of the light remains constant for the wall which is 4m away and 2m away.