Question

How will the interference pattern of Young's double slit change if one of the two slits is covered by a paper which transmits only half of the light intensity?

Answer 1

Let 'a' be the initial amplitude and I the intensity of the light wave from each slit. Then

`"I"_"max" = ("a" + "a")^2`

`= (sqrt"I" + sqrt"I")^2`

= 4 I

`"I"_"max" = (sqrt"I" - sqrt"I")^2` = 0

When one of slits is covered by paper, the intensity of light wave from this slit is `1/2`. While that of 2 the wave from the other slit is still I. Now we have,

`("I"_"max")"'" = (sqrt"I" + sqrt("I"/2))^2` = 2.914 I

`("I"_"min")"'" = (sqrt"I" - sqrt("I"/2))^2` = 0.086 I

The intensity of maxima will decrease from 4 I to 2.914 I and that of minima will increase from zero to 0.086 I.