Question

A double- slit experiment is performed with a coherent (single frequency/wavelength) beam of laser light.

1, suppose that the two slits are separated by a distance D= 0.1 mm; the distance (H) between the center of the pattern and the second ( m=2) bright region is 1.0 cm; and the distance(L) between the screen and the slits is 1.0 m. use the results of this experiment to determine the wavelength of the light.

2. Suppose that the frequency of the laster light is doubled. Determind the new spacing between the center of the pattern and the first fringe maximum

Answer 1

1) we know that fringe width is w= Lambda*L/D

==> distance between centralspot and 2nd maxima = 2w= 1 cm = 0.01 m

==> 2*Lambda*L/D= 0.01

==> 2*Lambda*1/0.1E-3 = 0.01

==> Lambda= (0.01*0.1E-3)/2=5E-7 m =500 nm

2) If frequency is doubled Lambda is halfed (since :: v=f*Lambda)

==> w= Lambda*L/D is also halfed

From the earlier part it was given

distance between centralspot and 2nd maxima =1 cm

==> w=0.5 cm

So new w (which is halfed) = 0.5/2 = 0.25 cm