Light originating from a point source strikes a screen. If the separation between the source and the screen is increased by 1 % , the illuminance decreases by approximately

Step-by-step solution

The illuminance E produced by a point source at a distance r is given by E = I r^2 , where I is the luminous intensity of the source. Taking the natural logarithm on both sides, we get E = I - 2 r . Differentiating for small changes, we obtain E E = -2 r r . Given that the separation r is increased by 1 % , we have r r 100 = 1 % . Therefore, the percentage change in illuminance is E E 100 = -2 ( r r 100 ) = -2(1 %) = -2 % . The negative sign indicates that the illuminance decreases. Thus, the illuminance decreases