Intensity of single slit and double slit problem

[desmond iking]

For a double slit experiemnt, the bright fringe has intensity of I, when one of the slit is covered, the intensity is 0.25I.
In my opinion, the slit now become single slit, so it has area of half of the initial area, but we know that power is the product of intensity x area, by keeping the power constant. So it should has intensity of 2I if one of the slit is covered?

 

[Orodruin]

The bright fringe has constructive interference when both slits are open, meaning that the amplitude is doubled. The intensity is the square of the amplitude and so
$$
I = A^2 = (2A_0)^2 = 4A_0^2 = 4I_0,
$$
where ##A## refers to the total amplitude and ##A_0## to that from one slit and the same for the intensities.

Where there is destructive interference, between the bright fringes, the amplitudes will cancel out and give you zero intensity.

 

[desmond iking]

Now one of the slit is closed , shouldn't the intensity of light is higher? Since the light ray now concentrate on smaller region.

 

[ehild]

The light beam can not concentrate itself and choose to go through the open slit. The part of the light beam falling on the open slit goes through, the other part reaching the screen is reflected, absorbed, but cannot go through.

ehild

 

[desmond iking]

The light beam can not concentrate itself and choose to go through the open slit. The part of the light beam falling on the open slit goes through, the other part reaching the screen is reflected, absorbed, but cannot go through.

ehild

no . i mean the light emerge form the slit concentrate ( a.k.a interfere) at smaller region , so the light energy now is distributed to smaller area... so the intensity is higher when one of the slit is closed.

 

[ehild]

No, equal energy of light goes through each slit. Two slits means twice energy passing through.
Think. When is more light in the room? I all the shutters are open or when only one is open?

ehild

 

[Orodruin]

no . i mean the light emerge form the slit concentrate ( a.k.a interfere) at smaller region , so the light energy now is distributed to smaller area... so the intensity is higher when one of the slit is closed.

The size of the illuminated region is essentially dependent on the slit size, the light wavelength, and the distance to the screen. Light from both slits will hit similar regions - otherwise there would be no interference.