Using a diffraction grating as a example, demonstrate that the frequency difference of two maxima resolved according to Rayleigh's criterion is equal to the reciprocal of the difference of propagation times of the exterme interfering oscillations, i.e. `delta v = 1//delta t`.

Which of the following statements are true (T) and which are false (F)? (i) Sum of the three sides of a triangle is less than the sum of its three altitudes. (ii) Sum of any two sides of a triangle is greater than twice the median drawn to the third side. (iii) Sum of any two sides of a triangle is greater than the third side. (iv) Difference of any two sides of a triangle is equal to the third side. (v) If two angles of a triangle are unequal, then the greater angle has the larger side opposite to it. (vi) Of all the line segments that can be drawn from a point to a line not containing it, the perpendicular line segment is the shortest one.

The energy difference of two stable orbit of hydrogen is 214 .68 kJmol^(-1) if the transition of electron take place than find the emitted frequency (Note : v = Delta E// h)

Demonstrate that when two harmonic oscillations are added, the time-averged energy of the resultant oscillation is equal to the sun of the energies of the consituent osciallations, if both of them (a) have the same direction and are incoherent, and all the values of the phase difference between the oscillations are equal probable, (b) are mutually perpendicular, ahve teh same frequency and an arbitary phase difference.

The wavelength of one line in the visible region o fthe atmoic spectrum of hydrogen is 6.5xx10^(-7)m . This radiation is emitted when electron in a hydrogen atom goes from a high enegry state to a lower energy state. Calculate the difference in enegry between the two states. Strategy: According to the Bohr frequency rule, if the electron jumps from one orbit whose quantum number is n_(1) to a second orbit whose quantum number is n_(f) , the difference in enegry (DeltaE) is related to the frequency (v) of the radiation which in turn is related to the wavelength (lambda) : ? DeltaE = hv and v = (c)/(lambda) Thus, DeltaE = (hc)/(lambda)

Student I, II and III perform an experiment for measuring the acceleratioon due to gravity (g) using a simple pendulum . Theu use different lengths of the pedulum and /or record time for different number of oscillations . The observation are shoen in the table . Least count for length =0.1cm Least count for time =0.1s If E_(I) , E_(II) and E_(III) are the percentage errors in g,i.e (Deltag)/(g)xx100 for students I, II, and III respectively ,