To determine how to maintain equal illumination across all areas of the stage when the distance between the lights and the stage is doubled, we need to understand the inverse square law of illumination.

Concept Explanation:

The illumination (\(E\)) on a surface from a point light source is inversely proportional to the square of the distance (\(d\)) from the light source. Mathematically, this is expressed as:

\(E \propto \frac{I}{d^2}\)

Where \(I\) is the luminous intensity of the light source.

If the distance is doubled, the new distance (\(d'\)) becomes \(2d\). Thus, the new illumination \(E'\) becomes:

\(E' = \frac{I}{(2d)^2} = \frac{I}{4d^2}\)

This shows that the illumination is reduced to a quarter of its original value (\(\frac{1}{4}\) of \(E\)) if the distance is doubled.

Solution:

To maintain the same level of illumination, we need to compensate for the reduced illumination by increasing the luminous intensity. From the relationship above, to restore \(E\) to its original level when \(E'\) is \(\frac{1}{4}\) of \(E\), the luminous intensity needs to be quadrupled:

\(I' = 4I\)

This means we must increase the luminous intensity of each light source by a factor of four to maintain equal illumination.

Conclusion:

The correct action, according to the laws of illumination, is to increase the luminous intensity of each light source by a factor of four. This is why the correct answer is Option B.

Other options are incorrect because:

• Increasing the angle of incidence does not directly change the illumination level based on distance adjustments.
• Doubling the luminous intensity is insufficient as it doesn't compensate enough when the distance squared factor reduces the illumination to a quarter.
• Using half the number of lights will decrease illumination further, not maintain it.