A single slit of width d = 0.07 mm is illuminated by light of two wavelengths, ?

Question

A single slit of width d = 0.07 mm is illuminated by light of two wavelengths, ? = 464 nm and ? = 664 nm. The diffraction pattern appears on a screen 1.38 m away.

1)

?464 = Rad

2) ?664 = Rad

3)

Calculate the width of the central bright fringe for each wavelength.

d464 = m

4)

d664 = m

A single slit of width d = 0.07 mm is illuminated by light of two wavelengths, ? = 464 nm and ? = 664 nm. The diffraction pattern appears on a screen 1.38 m away. Calculate the angles at which the third dark fringe appears for each wavelength.? 664 = Rad Calculate the width of the central bright fringe for each wavelength. d464 = m d664 = m

Explanation / Answer

d = 0.07 mm
?1 = 464 nm = 4.64 x 10^-4 mm
?2 = 664 nm = 6.64 x 10^-4 mm

1) d sin ? = n ?
---> sin ?1 = 3 * 4.64 x 10^-4/0.07 = 0.0198
?1 = arc sin (0.0198) = 1.134

2)
--> sin ?2 = 3 * 6.64 x 10^-4/0.07 = 0.0284
?2 = arc sin (0.0284) = 1.627

3)
b) d *y1/L = n ?1
--> y1 = n* ? 1* L/d
= 1 * 4.64 x 10^-4 * 1380/0.07 = 9.147 mm
the width of the central bright fringe : 2 * 9.147 = 18.29 mm

4)
--> y2 = n* ? 21* L/d
= 1 * 6.64 x 10^-4 * 1380/0.07 =13.09 mm
the width of the central bright fringe : 2 * 13.09 = 26.18 mm

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