Show that maximum intensity in interference pattern is four times the intensity due to each slit. Hence show that interference involves only redistribution of energy.

Explanation

Suppose the amplitude of waves from each slit is a. Therefore, intensity due to each slit `= a^(2)`. When interference is destructive, the resulant amplitude `= a - a =0`
`:.` Minimum intensity `= 0`
When interference is constructive, the resultant amplitude `= a + a = 2 a`
`:.` Maximum intensity `= (2 a)^(2) = 4 a^(2) = 4` time the intensity due to each slit, which was to be proved.
Also, average intensity in the interference pattern `= (0 + 4 a^(2))/(2) = 2 a^(2) =` sum of intensity due to two slits`.
Hence we conclude that interference involves only redistribution of energy keeping the total energy fixed.