Long Answer Type(a) Draw a labelled diagram of a moving coil galvanometer. Describe briefly its principle and working.
(b) Answer the following:
(i) Why is it necessary to introduce a cylindrical soft iron core inside the coil of a galvanometer?
(ii) Increasing the current sensitivity of a galvanometer may not necessarily increase its voltage sensitivity. Explain, giving reason.
(a) In Young's double slit experiment, describe briefly how bright and dark fringes are obtained on the screen kept in front of a double slit. Hence obtain the expression for the fringe width.
(b) The ratio of the intensities at minima to the maxima in the Young's double slit experiment is 9: 25. Find the ratio of the widths of the two slits.
a)
Let S1 and S2 be two coherent sources separated by a distance d.
Let the distance of the screen from the coherent sources be D. Let point M be the foot of the perpendicular drawn from O, which is the midpoint of S1 and S2 on the screen. Obviously point M is equidistant from S1 and S2. Therefore the path difference between the two waves at point M is zero. Thus point M has the maximum intensity.
Now, Consider a point P on the screen at a distance y from M. Draw S1N perpendicular from S1 on S2 P. 
The path difference between two waves reaching at P from S1 and S2 is given by, 
Since, D >> d, so 
is very small.
For dark fringe, path difference is an odd multiple of half wavelength.
So, we have 
Let, 
be the distance of two consecutive fringes. Then, we have
Fringe width is same for both bright and dark fringe.
b)
Give, ratio of minima to maxima intensity is given by, 9:25
That is, 
(a) Describe briefly how a diffraction pattern is obtained on a screen due to a single narrow slit illuminated by a monochromatic source of light. Hence obtain the conditions for the angular width of secondary maxima and secondary minima.
(b) Two wavelengths of sodium light of 590 nm and 596 nm are used in turn to study the diffraction taking place at a single slit of aperture 2 × 10−6 m. The distance between the slit and the screen is 1·5 m. Calculate the separation between the positions of first maxima of the diffraction pattern obtained in the two cases.
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