Question

One of the two slits in a Young’s experiment is painted over so that it transmits only one-half the intensity of the other slit. As a result:

A. the fringe system disappears
B. the bright fringes get brighter and the dark ones get darker
C. the fringes just get dimmer
D. the dark fringes just get brighter
E. the dark fringes get brighter and the bright ones get darker

Answer 1

B. the bright fringes get brighter and the dark ones get darker

Step-by-step explanation:

Let us consider when the intensities are equal, we use the equation

`I_(max) = I_(1) + I_(2) + 2√(I*I)` for light fringes and,

`I_(min) = I_(1) + I_(2) - 2√(I*I)` for dark fringes

where
`I_(1)` and
`I_(1)` are the light intensities from the first and second slits respectively.

For the first case where the light from the two slits have the same intensities, we can say both have intensity
`I`

`I_(max) = I + I + 2√(I*I)` =
`2I + 2I = 4I`

`I_(min) = I + I - 2√(I*I) = 2I - 2I = 0`

For the case where one of the intensities has half the intensity of the other.

one has intensity
`I` and the other one has intensity
`(I)/(2)`

inserting, we have

`I_(max) = I + (I)/(2) + 2\sqrt{I*(I)/(2)} = 2.932I`

`I_(min) = I + (I)/(2) - 2\sqrt{I*(I)/(2)} = 0.068I`

this shows that the bright fringes get brighter and the dark ones get darker.