Question

Need help to solve this question.

Answer 1

The intensity becomes one fourth when the distance is doubled.

Explanation:

The statement is

Intensity of light
`l` varies inversly as the square of the distance
`d`

So we get

`l=(k)/(d^2)`

Now for distance 12in let the intensity be
`l_(1)`

So we get

`l_(1)=(k)/(12^2)`

`l_(1)=(k)/(144)` ...(1)

For distance 24in, let the intensity be
`l_(2)`

We get

`l_(2)=(k)/(24^2)`

`l_(2)=(k)/(576)` ....(2)

Dividing (1) by (2) we get

`(l_(1))/(l_(2))=( (k)/(144))/( (k)/(576))=(576)/(144)`

`(l_(1))/(l_(2))=4`

`l_(1)=4l_(2) \ or \ l_(2) = (1)/(4)l_(1)`

Hence the intensity becomes one fourth