Consider a thick equiconvex lens of refractive index 1 \cdot 5 as shown in the figure. The magnitude of the radii of curvatures of the two surfaces is 5\text{ cm}. The thickness of the lens is 1\text{ cm} and the lens is placed in the air. Obtain the system matrix and determine the focal length and the position of unit planes :
An achromatic doublet of focal length 25\text{ cm} is to be made by placing a convex lens of borosilicate crown glass in contact with a diverging lens of dense flint glass. Assuming n_r = 1 \cdot 61864, n_b = 1 \cdot 62468, n_r' = 1 \cdot 71426 and n_b' = 1 \cdot 72906, calculate the focal length of each lens. Here, the unprimed and the primed quantities refer to the borosilicate crown glass and dense flint glass respectively.
A length of 25\text{ cm} of a solution containing 50\text{ gm} of solute per litre causes a rotation of the plane of polarization of light by 5^\circ. Find the rotation of the plane of polarization by a length of 75\text{ cm} of the solution containing 100\text{ gm} of solute per litre.
Explain the formation of spectra by a plane diffraction grating. What particular spectra would be absent if the width of the slit is equal to the width of the opaque spacing between any two consecutive slits?
In the above experiment, a shift of 100 fringes is obtained when all the gas is removed from the tube. Calculate the refractive index of the gas if the wavelength of light used is 6000\text{ \AA} and the length of the tube is 10\text{ cm}.
The coherence length and the bandwidth of a light source is 3\text{ km} and 1 \times 10^{-5}\text{ nm}, respectively. Determine its wavelength and the pulse duration.
Discuss the phenomenon of birefringence in a crystal. What do you understand by positive and negative crystals ? If the refractive indices of a calcite crystal for E-ray and O-ray are 1\cdot 488 and 1\cdot 658, respectively, then calculate the thickness of the crystal for which it can work as
(i) quarter wave plate,
(ii) half wave plate. (Wavelength of the light is 5890\text{ \AA})
A transmission hologram is recorded in a medium of refractive index 1\cdot 15. If the spacing between the two consecutive maxima is 557\text{ nm} and the angle of incidence of reference and object waves from the reference axis (say z-direction) is 30^\circ, find the wavelength of the light source.
What do you understand by missing orders in a double-slit diffraction pattern ? Obtain condition for missing orders in a double-slit Fraunhofer diffraction pattern, if the slit width and the separation between the slits are equal. In a double-slit diffraction experiment, if the slit widths are 0\cdot 20\text{ mm} and they are 0\cdot 10\text{ mm} apart, find the missing orders.
State Fermat's principle. Using this principle, establish the Snell's law of refraction.
What is forced oscillation ? Write its equation of motion and obtain the general solution. Discuss the condition for the resonance.
In a Newton's ring experiment, explain the following :
(i) Why are the fringes circular ?
(ii) Why is the central spot dark as seen by reflection ?
(iii) How can one obtain Newton's ring with bright centre ?
A tuning fork A produces 6 beats per second with another tuning fork B of frequency 508\text{ Hz}. When the prongs of A are loaded with a little wax, number of beats heard are 4 per second. Find the frequency of A before it was loaded with wax.
Consider that a continuous laser beam which is assumed to be perfectly monochromatic with a wavelength of 6500\text{ \AA} is chopped into 2\text{ ns} pulses using a shutter. Calculate the number of photons in each pulse, if the power of each pulse is 5\text{ mW}.
What is holography ? Briefly discuss the applications of holography.
What is achromatism ? Obtain the condition for achromatism of two thin lenses separated by a distance of x metres.
What is the principle of propagation in optical fibers ? Explain with the help of neat diagram, the ray propagation in Step index and Parabolic index optical fibers. How can pulse dispersion be minimized using Parabolic index optical fibers ?
What are beats ? A tuning fork gives 6 beats per second with 25\cdot 4\text{ cm} length of stretched sonameter wire. The same 6 beats are heard per second when the length of the same wire is reduced to 24\cdot 6\text{ cm}. Calculate the frequency of the tuning fork.
Two glasses have dispersive powers in the ratio 2 : 3. These glasses are used in the manufacture of an achromatic contact objective of focal length 50\text{ cm}. What are the focal lengths of the lenses ?
What is the Resolving power of a grating ? Obtain an expression for the Resolving power of a grating, based on Rayleigh's criterion of resolution.
