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(Solved): All A pair of narrow slits is positioned 1.70 m from a screen and illuminated with light made up of ...


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A pair of narrow slits is positioned 1.70 m from a screen and illuminated with light made up of two wavelengths 512.00 nm and 623.20 nm.

First a filter is used to block the 623.20 nm light from reaching the screen. The resulting interference maxima are found to be separated by s = 0.90 mm.

a) What is in meters the separation of the slits?

We now remove that filter and place a filter that blocks the 512.00 nm light.

b) What is in mm the obtained fringe separation?

We remove both filters.

c) What is in meters the separation on the screen of first bright maxima due to both wavelengths?

d) What is in meters the separation on the screen of fourth bright maxima due to both wavelengths?



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A)

To find the separation of the slits, we can use the formula for the fringe separation in a double-slit interference pattern:

  


where,
* S is the fringe separation,
* ? is the wavelength of the light,
* L is the distance from the slits to the screen,
* d is the separation of the slits.

Given:
?1 = 623.20 nm =    (wavelength of light after the filter) ?2 = 512.00 nm =    (wavelength of light after the second filter) L =   (distance from slits to screen) s = 0.90 mm =    (fringe separation after the first filter)
Using the given values for ?1 and L, we can rearrange the formula to solve for d:

  

Substituting the values, we get:

  
  

So, the separation of the slits is   meters.

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