A lamp is moved from 26 cm to 90 cm above the pages of a book. Compare the illumination on the book before and after the lamp is move.
The illumination varies as the inverse square of the distance..
1/(26)^2
1/(90)^2
.00148
1.234e-4
To compare the illumination on the book before and after the lamp is moved, we need to understand the relationship between the distance of the lamp from the book and the intensity of the illumination.
In this case, the lamp is moved from 26 cm to 90 cm above the pages of the book. The distance between the lamp and the book has increased. When the distance between the lamp and the book increases, the intensity of the illumination decreases.
To understand this relationship, we can make use of the inverse square law, which states that the intensity of light is inversely proportional to the square of the distance. Mathematically, this can be expressed as:
I ∝ 1/d^2
Where I represents intensity and d represents distance.
Let's compare the illumination on the book before and after the lamp is moved:
Before the lamp is moved:
Distance (d1) = 26 cm
Intensity (I1) = 1/(26^2)
After the lamp is moved:
Distance (d2) = 90 cm
Intensity (I2) = 1/(90^2)
To compare the two intensities, we can calculate the ratio of I2 to I1:
(I2/I1) = (1/(90^2))/(1/(26^2))
= (1/(8100))/(1/(676))
= 676/8100
= 0.0832
Therefore, the illumination on the book after the lamp is moved is approximately 8.32% of the illumination before the lamp is moved. In other words, the illumination on the book decreases significantly when the lamp is moved farther away.