A battery operated tourch is adjusted to send and almost parallel beam of light. It produces an illuminance of 40 lux when the light falls on a wal 2m away. The illuminance produced when it fals on a wal 4 m away is close to

Options

A. 40 lux
B. 20 lux
C. 10 lux
D. 5 lux

Answer

To solve the problem, we need to understand how illuminance behaves with distance when light is emitted in a parallel beam.

### Step-by-Step Solution:

1. **Understand the Concept of Illuminance**:
Illuminance (E) is defined as the luminous flux (Φ) per unit area (A) over which the light is distributed. The formula is given by:
\[ E = \frac{\Phi}{A} \]

2. **Identify the Given Information**:
- The illuminance at a distance of 2 meters is 40 lux.
- We need to find the illuminance at a distance of 4 meters.

3. **Consider the Nature of the Light Source**:
The problem states that the torch produces an almost parallel beam of light. This means that the light rays do not spread out significantly as they travel away from the source.

4. **Analyze the Effect of Distance on Illuminance**:
For a parallel beam of light, the area over which the light is distributed does not increase significantly with distance. Therefore, the illuminance remains constant regardless of the distance from the source.

5. **Calculate the Illuminance at 4 Meters**:
Since the illuminance at 2 meters is 40 lux and the beam is parallel, the illuminance at 4 meters will also be:
\[ E = 40 \text{ lux} \]

### Final Answer:
The illuminance produced when the light falls on a wall 4 meters away is **40 lux**.

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