If, in a two-slit interference pattern, there are bright fringes within the first side peak of the diffraction envelope and diffraction minima coincide with two-slit interference maxima, then what is the ratio of slit separation to slit width?
The ratio of the slit separation to the slit width is .
In a two-slit interference pattern, there are bright fringes within the first side peak of the diffraction envelope.
The angular distance of the order diffraction minima is given by
Here, is the wavelength of the incident light and is the slit width.
The angular distance of the order interference maxima is given by
Here, is the wavelength of the incident light and is the separation between the two slits.
The interference maxima coincide with the diffraction minima. From equations (i) and (ii) the angular distance of the diffraction minima and the interference maxima is
Divide the two equations to get
Thus, the required ratio is .
Figure shows a red line and a green line of the same order in the pattern produced by a diffraction grating. If we increased the number of rulings in the grating – say, by removing tape that had covered the outer half of the rulings – would (a) the half-widhts of the lines and (b) the separation of the lines increase, decrease, or remain the same? (c) Would the lines shift to the right, shift to the left, or remain in place
(a) Figure 36-34a shows the lines produced by diffraction gratings A and B using light of the same wavelength; the lines are of the same order and appear at the same angles . Which grating has the greater number of rulings? (b) Figure 36-34b shows lines of two orders produced by a single diffraction grating using light of two wavelengths, both in the red region of the spectrum. Which lines, the left pair or right pair, are in order with greater m? Is the center of the diffraction pattern located to the left or to the right in (c) Fig. 36-34a and d) Fig. 36-34b?
Monochromatic light (wavelength ) is incident perpendicularly on a single slit (width ). A screen is placed parallel to the slit plane, and on it the distance between the two minima on either side of the central maximum is .
(a) What is the distance from the slit to the screen? (Hint: The angle to either minimum is small enough that .)
(b) What is the distance on the screen between the first minimum and the third minimum on the same side of the central maximum?
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