The mathematical expression for one dimensional wave travelling along the positive x-direction is given as
y(x,t) = 0.02 sin(42 x -1886t)m
where x is in meters and t is in seconds. Determine the direction of propagation of the wave and calculate its amplitude, wavelength, frequency and velocity.
The given mathematical expression for a one-dimensional wave is \(y(x, t) = 0.02 \sin(42x - 1886t) \) meters. This expression represents a sinusoidal wave that is a function of both position (\(x\)) and time (\(t\)).
Direction of Propagation:
The expression \(42x - 1886t\) inside the sine function indicates the phase of the wave. The coefficient of \(x\) is positive (42x), and the coefficient of \(t\) is negative (-1886t). This implies that the _________ __________ __________ ______ _____ _____ __________ ___ ___.
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Explain the meaning of coherence length.
The Fraunhofer diffraction pattern due to a single slit of width 0.4 cm is obtained with the help of a lens of focal length 30 cm. If the wavelength of light used is 5890 Å, calculate the distance of the first dark fringe and the consecutive bright fringe from the axis.
The electric field vectors of two light waves propagating along the positive z- direction are given as
where and
are unit vectors along x and y-axes, respectively. Show that when these two waves superpose, we obtain elliptically polarised light. Also show that the linear and circular polarisations are special cases of elliptical polarisation.
What do you understand by spatial and temporal coherence?
In the Fraunhofer diffraction pattern due to a single slit, the intensity of the central spot is maximum. Explain on the basis of geometrical considerations.
The radius of the fifth zone of a zone plate is 2 mm. Considering the zone plate as a converging lens, calculate its focal length for light of wavelength 4800 Å.
ii) Newton’s rings are formed in reflected light of wavelength 5890 10-8cm with a liquid between the plane and curved surfaces. The diameter of the fifth ring is 0.3 cm and the radius of curvature of the curved surface is 100 cm. Calculate the refractive index of the liquid, when the ring is bright.