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Light from two lasers is incident on an opaque barrier with a single slit of width 4.0 x 10^-4 m. One laser emits light of wavelength 480 nm and the other is 640 nm. A screen to view the light intensity pattern is 2.0 m behind the barrier. The distance from the center of the pattern to the nearest completely dark spot (dark for both colors) is ____ cm. (include 2 digits after the decimal point)

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Answer:

a) y = 2.4 x 10ā»Ā³ m = 0.24 cm

b) y = 3.2 x 10ā»Ā³ m = 0.32 cm

Explanation:

The formula of Young's Double Slit experiment will be used here:

[tex]y = \frac{\lambda L}{d}\\\\[/tex]

where,

y = distance between dark spots = ?

Ī» = wavelength

L = distance of screen = 2 m

d = slit width = 4 x 10ā»ā“ m

a) FOR Ī» = 480 nm = 4.8 x 10ā»ā· m:

[tex]y = \frac{(4.8\ x\ 10^{-7}\ m)(2\ m)}{4\ x\ 10^{-4}\ m}[/tex]

y = 2.4 x 10ā»Ā³ m = 0.24 cm

a) FOR Ī» = 640 nm = 6.4 x 10ā»ā· m:

[tex]y = \frac{(6.4\ x\ 10^{-7}\ m)(2\ m)}{4\ x\ 10^{-4}\ m}[/tex]

y = 3.2 x 10ā»Ā³ m = 0.32 cm

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