In Young\'s experiment a mixture of orange light (611 nm) and blue light (471 nm

Question

In Young's experiment a mixture of orange light (611 nm) and blue light (471 nm) shines on the double slit. The centers of the first-order bright blue fringes lie at the outer edges of a screen that is located 0.620 m away from the slits. However, the first-order bright orange fringes fall off the screen. By how much and in which direction (toward or away from the slits) should the screen be moved, so that the centers of the first-order bright orange fringes will just appear on the screen? It may be assumed that 0 is small, so that sin theta = tan theta. distance 0.478 m direction

Explanation / Answer

Initial distance between the slits and the screen be D = 0.62m, let the distance between the slits be d.

Let b be wavelength of the blue light and o be wavelength of the orange light

Position of first order bright fringe for blue light is given by

y = Db/d, which is obtained at the edge of the screen. ------------ (1)

So for the center of the first order bright orange fringe to just appear on the screen, i.e., on the edge, y has to be same for what found for blue light above.

Now suppose the screen is moved towards the slits by a distance b so that the first order bright orange fringe just appear on the screen on its edge. Then we have

y = (D-b)o/d ------------- (2)

from equations (1) and (2) we get:

Db/d = (D-b)o/d

or Db = (D-b)o

or (1 - b/D) = b/o

or b/D = 1 -  b/o

or b/D = 1 - (471mm)/(611mm)

or b/D = 140/611

or b = (0.62m)(140/611) = 0.142m

We asumed that the screen is moved towards the slit by distance b and got the value b to be positive. That means our assumption was correct.

So the screen to be moved 0.142m towards the slit.

This concludes the answers. Check the answer and let me know if it's correct. If you need anymore clarification I will be happy to oblige....

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