A pair of narrow, parallel slits separated by a distance of 0.256 mm are illumin

Question

A pair of narrow, parallel slits separated by a distance of 0.256 mm are illuminated by the green component from a mercury vapor lamp of wavelength 545.3 nm. The interference pattern is observed on a screen 1.34 m from the plane of the parallel slits.

A. Find the distance from the central maximum to the first bright region on either side of the central maximum. (Answer in units of mm.)

B. Find the distance between the first and second dark bands in the interference pattern. (Answer in units of mm.)

Explanation / Answer

The seperation of the slits is d = 0.256 mm

d = 0.256 mm (1 m /1000 mm) = 0.000256 m
The distance of the slits from the screen is D = 1.34 m
The wavelength of the light used is = 545.3 nm
= 545.3 nm(1 m/109 nm)
= 545.3*10-9 m
------------------------------------------------------------------------------------------------------------

(a)

The condition for the constructive interference is
y = mD/d
here y is the distance of the mth bright fringe from the central bright
For m=1
y1 = (1)(545.3*10-9 m)(1.34 m)/(0.000256 m)
y1 = 2.854*10-3 m
y1 = 2.854 mm

----------------------------------------------------------------------------------------------------------

(b)

The distance between the first and second dark fringes is given by
= D/d
= (545.3*10-9 m)(1.34 m)/(0.000256 m)
= 2.854*10-3 m
= 2.854 mm The seperation of the slits is d = 0.256 mm

d = 0.256 mm (1 m /1000 mm) = 0.000256 m
The distance of the slits from the screen is D = 1.34 m
The wavelength of the light used is = 545.3 nm
= 545.3 nm(1 m/109 nm)
= 545.3*10-9 m
------------------------------------------------------------------------------------------------------------

(a)

The condition for the constructive interference is
y = mD/d
here y is the distance of the mth bright fringe from the central bright
For m=1
y1 = (1)(545.3*10-9 m)(1.34 m)/(0.000256 m)
y1 = 2.854*10-3 m
y1 = 2.854 mm

----------------------------------------------------------------------------------------------------------

(b)

The distance between the first and second dark fringes is given by
= D/d
= (545.3*10-9 m)(1.34 m)/(0.000256 m)
= 2.854*10-3 m
= 2.854 mm The seperation of the slits is d = 0.256 mm

d = 0.256 mm (1 m /1000 mm) = 0.000256 m
The distance of the slits from the screen is D = 1.34 m
The wavelength of the light used is = 545.3 nm
= 545.3 nm(1 m/109 nm)
= 545.3*10-9 m
------------------------------------------------------------------------------------------------------------

(a)

The condition for the constructive interference is
y = mD/d
here y is the distance of the mth bright fringe from the central bright
For m=1
y1 = (1)(545.3*10-9 m)(1.34 m)/(0.000256 m)
y1 = 2.854*10-3 m
y1 = 2.854 mm

----------------------------------------------------------------------------------------------------------

(b)

The distance between the first and second dark fringes is given by
= D/d
= (545.3*10-9 m)(1.34 m)/(0.000256 m)
= 2.854*10-3 m
= 2.854 mm The seperation of the slits is d = 0.256 mm

d = 0.256 mm (1 m /1000 mm) = 0.000256 m
The distance of the slits from the screen is D = 1.34 m
The wavelength of the light used is = 545.3 nm
= 545.3 nm(1 m/109 nm)
= 545.3*10-9 m
------------------------------------------------------------------------------------------------------------

(a)

The condition for the constructive interference is
y = mD/d
here y is the distance of the mth bright fringe from the central bright
For m=1
y1 = (1)(545.3*10-9 m)(1.34 m)/(0.000256 m)
y1 = 2.854*10-3 m
y1 = 2.854 mm

----------------------------------------------------------------------------------------------------------

(b)

The distance between the first and second dark fringes is given by
= D/d
= (545.3*10-9 m)(1.34 m)/(0.000256 m)
= 2.854*10-3 m
= 2.854 mm
(b)

The distance between the first and second dark fringes is given by
= D/d
= (545.3*10-9 m)(1.34 m)/(0.000256 m)
= 2.854*10-3 m
= 2.854 mm

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