Answer to Question #144349 in Optics for John Li

Question

An adjustable monochromatic laser beam is directed at two slits spaced 0.400 mm apart. A screen 3 m away displays the interference pattern due to the diffraction of the beam by the two slits. If the laser wavelength is changed uniformly from 500 nm to 630 nm over 5 s, what is the speed of the first maximum intensity line from the center? Is it moving toward the center or away from the center?

Answer 1

As per the given question,

Distance between the two slits $(d)=0.4mm = 4\times 10^{-4}m$

Distance between the slits and the screen $(D)=3m$

Initial wavelength $(\lambda_i)=500nm = 5\times 10^{-7}m$

Final wavelength $(\lambda_f) =630nm = 6.3\times 10^{-7}m$

Time (t)=3 sec

distance of the first maximum central intensity $(y_i) = \frac{n \lambda_i D}{d}$

Now, substituting the values, $(y_i)=\frac{ 5\times 10^{-7}m\times 3}{4\times 10^{-4}}m$

$\Rightarrow y_i=3.75\times 10^{-3}m$

$\Rightarrow y_i =3.65mm$

Similarly,$y_f=\frac{6.3\times 10^{-7}\times3}{4\times 10^{-4}}m$

$y_f=4.724mm$

Hence, the speed of the first maximum intensity $=\frac{4.724-3.65}{3}m/s$

$=0.358m/s$

It is moving away from the center, because the wavelength is increasing.