Chapter 8.4, Problem 2E

To determine

Toinfer : the intensity of light is greater or less than $25$ according to the given equation.

To explain the intensity at the edge of the table should be greater than or less than the intensity at the corner.

To infer the equation is correct or not.

Answer to Problem 2E

According to the given equation, the intensity of light is greater than $25$ which is incorrect as the intensity of light ( I ) is inversely proportional to square of the distance ( d ) of the object from the source, so it should be less at the edge of the table.

The given equation is incorrect.

Explanation of Solution

Given information :

Consider Problem $6$ on page $362$ ,

A light hangs $4.8$ ft. above the center of a circular table $7.2$ ft. in diameter.

The illumination at the center of the table is $25$ lux.

The given equation:

  $\frac{I}{{(6.0)}^2}=\frac{25}{{(4.8)}^2}$

Here I is the intensity of light at the edge of the table.

As per the problem,

According to the given equation:

  $\begin{array}{l}\frac{I}{{(6.0)}^2}=\frac{25}{{(4.8)}^2}\\ I=\frac{25{(6.0)}^2}{{(4.8)}^2}\\ I=39.063\end{array}$

The intensity of light is greater than $25$ .

Intensity of light ( I ) is inversely proportional to square of the distance ( d ) of the object from the source.

  $I=\frac{k}{d^2}$ wherek is the proportionality constant.

So, as the distance from the light source increases, the intensity decreases.

Therefore, at the edge of the table the intensity should be less than the intensity of light at the center, as the center of the table is closer to the light source than the edge.

The given equation is incorrect as it shows intensity of light ( I ) is directly proportional to square of the distance ( d ) of the object from the source.