Light from a point source falls on a small area placed perpendicular to the incident light. if the area is rotated about the incident light by an angle of ~60∘, by what fraction will the illuminance change ?

Explanation

To solve the problem of how the illuminance changes when a small area is rotated about the incident light by an angle of 60 degrees, we can follow these steps:

### Step 1: Understand the Concept of Illuminance
Illuminance (E) is defined as the power of light (P) received per unit area. The formula for illuminance from a point source is given by:
\[ E = \frac{P}{4 \pi D^2} \]
where:
- \( P \) is the power of the light source,
- \( D \) is the distance from the light source to the area.

### Step 2: Analyze the Initial Condition
Initially, the small area is placed perpendicular to the incident light. In this position, the distance \( D \) from the point source to the area is at its minimum, and the illuminance can be calculated using the formula above.

### Step 3: Consider the Rotation of the Area
When the area is rotated by an angle of 60 degrees, it is still illuminated by the same point source. However, we need to determine how this rotation affects the distance \( D \) and consequently the illuminance.

### Step 4: Determine the New Distance
When the area is rotated, the distance \( D \) from the light source to the area will change. However, due to the geometry of the situation, the distance \( D \) will not change significantly as the area is small and the rotation is about the line of sight from the point source.

### Step 5: Evaluate the Effect on Illuminance
Since the illuminance formula depends on \( D^2 \) and the angle of incidence does not affect the distance significantly for a small area, we can conclude that the illuminance remains effectively unchanged.

### Step 6: Conclusion
Thus, the fraction by which the illuminance changes is:
\[ \text{Fraction change} = \frac{\Delta E}{E} = 0 \]
This means that the illuminance does not change when the area is rotated by 60 degrees.

### Final Answer
The fraction by which the illuminance changes is 0.

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