Q. 264.2( 12 Votes )

(a) Describe any two characteristic features which distinguish between interference and diffraction phenomena. Derive the expression for the intensity at a point of the interference pattern in Young’s double slit experiment.

(b) In the diffraction due to a single slit experiment, the aperture of the slit is 3 mm. If monochromatic light of wavelength 620 nm is incident normally on the slit, calculate the separation between the first order minima and the 3rd order maxima on one side of the screen. The distance between the slit and the screen is 1.5 m.

OR

(a) Under what conditions is the phenomenon of total internal reflection of light observed ? Obtain the relation between the critical angle of incidence and the refractive index of the medium.

(b) Three lenses of focal lengths +10 cm, –10 cm and +30 cm are arranged coaxially as in the figure given below. Find the position of the final image formed by the combination.



Answer :

(a)



Consider two coherent sources of light S1 and S2. The two sources of light will produce an interference pattern on the screen GG’. Consider a point P on the screen. Let be the phase difference due to the path difference S2P - S1P .



The electric filed from the light at each of the sources S1 and S2 can be written as,




where each source of light has maximum electric filed strength .


At P, by principle of superposition,




As intensity is the square of the amplitude,



Note that . Hence,



(b)


Given,


Size of aperture,
Wavelength of light,

Distance from screen,


Size of one maxima/minima (except the central),




Now, the required patriation has four fringes. Hence, the distance is:



OR


(a)


The conditions for total internal reflection are:


(i) Light must be trying to travel from optically denser medium to optically lighter medium.


(ii) The angle of incidence must be greater than a certain angle known as critical angle.


Derivation:


Suppose light is travelling from medium 1 to medium 2. When light strikes the surface separating the media, some of it refracts and some of it reflects. If we keep increasing the angle of incidence, the refracted ray becomes parallel to the surface. This value of angle of incidence is known as the critical angle. If we increase the angle of incidence, even further, we will have a reflected ray and no refracted ray. Thus, we will have total internal reflection.



Let us consider the condition when the angle of incidence is equal to critical angle, .


By Snell’s law,



where and are the refractive indices of medium 1 and medium 2 respectively. Let be the refractive index of 1 with respect to 2.




Thus, we have obtained the required relation.


(b)


Concepts/Formulas used:


The lens equation:


The lens formula is:
where f is the focal length, u is the object distance and v is the image distance. All quantities are measured with the cartesian sign convention (the sign convention in NCERT).


Let us consider the lenses one by one.


The first lens forms an image of the given object.


Here,
Object distance,

Focal length,


Using the lens equation,







The image I1 formed by the first lens acts as an object for the second lens.


Here,
Object distance,

Focal length,






Let us now consider the third lens. It is a converging lens as it has a positive focal point. An object at infinity would have its image at the focal point (either of the focal points as the object is in either direction).


Hence, the final image is formed at 30cm from the third lens at either side.


Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
PREVIOUS(a) In a series LCR circuit connected across an ac source of variable frequency, obtain the expression for its impedance and draw a plot showing its variation with frequency of the ac source.(b) What is the phase difference between the voltages across inductor and the capacitor at resonance in the LCR circuit ?(c) When an inductor is connected to a 200 V dc voltage, a current of 1A flows through it. When the same inductor is connected to a 200 V, 50 Hz ac source, only 0.5 A current flows. Explain, why ? Also, calculate the self inductance of the inductor.OR(a) Draw the diagram of a device which is used to decrease high ac voltage into a low ac voltage and state its working principle. Write four sources of energy loss in this device.(b) A small town with a demand of 1200 kW of electric power at 220 V is situated 20 km away from an electric plant generating power at 440 V. The resistance of the two-wire line carrying power is 0.5 Ω per km. The town gets the power from the line through a 4000-220 V step-down transformer at a sub-station in the town. Estimate the line power loss in the form of heat.NEXT(a) Describe briefly the process of transferring the charge between the two plates of a parallel plate capacitor when connected to a battery. Derive an expression for the energy stored in a capacitor.(b) A parallel plate capacitor is charged by a battery to a potential difference V. It is disconnected from battery and then connected to another uncharged capacitor of the same capacitance. Calculate the ratio of the energy stored in the combination to the initial energy on the single capacitor.OR(a) Derive an expression for the electric field at any point on the equatorial line of an electric dipole.(b) Two identical point charges, q each, are kept 2m apart in air. A third point charge Q of unknown magnitude and sign is placed on the line joining the charges such that the system remains in equilibrium. Find the position and nature of Q.
Related Videos
All About Faraday's law55 mins
Know all about Infertility39 mins
Revision Class | All Formulas of Electrodynamics63 mins
Get to know all about Immune SystemFREE Class
Know all about Colligative Properties50 mins
Know All About Types of Relations53 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
view all courses
RELATED QUESTIONS :