Question

Light from a point source falls on a screen.if the separation between the source and the screen is increased by $1\%$ the illuminance will decrease (nearly) by

• A. $0.5\%$
• B. $1\%$
• C. $2\%$
• D. $4\%$

Answer 1

Answer: (C)

$2\%$

Illuminance depends on inverse of area and area is proportional to $r^2$ where is r is distance from the source to the point .
$illuminance\propto \frac{1}{r^2}$
$\frac{\partial \left(illuminance\right)}{\partial x}=-\frac{2\delta r}{r}$
hence changing distance by $1$% the illuminance will differ by $-\frac{2\delta r\times 100}{r}=-2$%
i.e,illuminance will decrease by $2$%
option $C$ is correct