Question

RACTIC PTUDIES

DUULIITIUUS,

1. A lamp is moved from 30 cm to 90 cm above the pages of a book. Compare the

illumination on the book before and after the lamp is moved.

Answer 1

The illumination on the book before the lamp is moved is 9 times the illumination after the lamp is moved.

Step-by-step explanation:

The distance of the book before the lamp is moved,
`d_(b) = 30 cm`

The distance of the book after the lamp is moved,
`d_(a) = 90 cm`

Illumination can be given by the formula,
`E = (P)/(4 \pi d^(2) )`

Illumination before the lamp is moved,
`E_(b) = (P)/(4 \pi d_(b) ^(2) )`

Illumination after the lamp is moved,
`E_(a) = (P)/(4 \pi d_(a) ^(2) )`

`(E_(a))/(E_(b)) } = ((P)/(4 \pi d_(a) ^(2) ) )/((P)/(4 \pi d_(b) ^(2) ) )`

`(E_(a) )/(E_(b) ) = (d_(b) ^(2) )/(d_(a) ^(2)) \\(E_(a) )/(E_(b) ) = (30^(2) )/(90 ^(2))\\(E_(a) )/(E_(b) ) =(900 )/(8100)\\(E_(a) )/(E_(b) ) =(1 )/(9)`

`E_(b) = 9E_(a)`

The illumination on the book before the lamp is moved is 9 times the illumination after the lamp is moved.