Chapter 16, Problem 8STP

To determine

To choose: The correct option.

Answer to Problem 8STP

The correct option is $\text{B}$

Explanation of Solution

Given:

A illuminance of direct sunlight on Earth is about 1×10⁵ lx and a light on a stage has an intensity of 5×10⁶cd in a certain direction and the audience is to experience the illuminance as equal to that of Sun at a particular distance from the stage.

Formula used:

The illuminance of the light on a stage is equal to that of the sun and it can be expressed in terms of the luminous flux and distance between the stage and audience as,

  $E=\frac{P}{s^2}$

Calculation:

Substituting the illuminance as E=1×10⁵ lx and the luminous intensity as P=5×10⁶cd, the distance can be calculated as,

  $\begin{array}{c}{r}^2=\frac{P}{E}\\ =\frac{5\times {10}^6}{1\times {10}^5}\\ =50\\ r=7.07\\ \simeq 7\text{}\text{}\text{m}\end{array}$

Conclusion:

The correct option representing the distance between the stage and audience for the given illuminance is (B), $7\text{}\text{ m}$ .