Q24 of 26 Page 1

(i) State the essential conditions for diffraction of light.

(ii) Explain diffraction of light due to a narrow single slit and the formation of pattern of fringes on the screen.


(iii) Find the relation for width of central maximum in terms of wavelength ‘l’, width of slit ‘a’, and separation between slit and screen ‘D’.


(iv) If the width of the slit is made double the original width, how does it affect the size and intensity of the central band?


OR


(i) Draw a labelled schematic ray diagram of astronomical telescope in normal adjustment.


(ii) Which two aberrations do objectives of refracting telescope suffer from? How are these overcome in reflecting telescope?


(iii) How does the resolving power of a telescope change on increasing the aperture of the objective lens? Justify your answer.


The phenomenon that occurs when the light comes across the object and it obstructs is known as diffraction.


The essential condition for diffraction of light is given by,


• The wavelength of the light should always be comparable to the size of the object.


• In certain cases, it may occur is the size of the object is less than the wavelength of light.


(ii)



Let a set of parallel rays from lens L1 allows to fall on the slit which then works as secondary source using Huygens’s principle. The resultant intensity is maximum.


For secondary minima:


Consider the right-angle triangle ,



For first minima, n=1



Thus, for nth minima,



For secondary maxima:


The path difference at the point is given by,


…(n=1)


For n=2,



General formula for nth maxima is,



(iii) In right angle triangle COP,



As θ is very small, sin θ=tan θ



For central maxima,



(iv) The size of the central band is given by,



Thus, size of central band reduces to half.


OR


(i) The schematic ray diagrams of astronomical telescope are,



(ii) There are two types of aberrations of reflecting telescope:


Spherical aberration:


It is the defect in the lens that result in the focusing of the beam of light on the point after passing through the spherical surface.


Chromatic aberration:


It is the defect in the lens which results in the formation of the blurred and coloured image.


(iii)


• The resolving power of the telescope increases if the frequency of the incident light is increased.


• The resolving power of the telescope does not change if the focal length of the objective is increased.


• The resolving power of the telescope halved if the aperture of the objective is halved.


More from this chapter

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22

(i) Define self-inductance. Write its SI units.

(ii) A long solenoid with 15 turns per cm has a small loop of area 2.0 cm2 placed inside the solenoid normal to its axis. If the current carried by the solenoid changes steadily from 2.0 A to 4.0 A in 0.1 s, what is the induced emf in the loop while the current is changing?


 23

Gautam went for a vacation to the village where his grandmother lived. His grandmother took him to watch ‘nautanki’ one evening. They noticed a black box connected to the mike lying nearby. Gautam’s grandmother did not know what that box was. When she asked this question to Gautam, he explained to her that it was an amplifier.

(i) Which values were displayed by the grandmother? How can inculcation of these values in students be promoted?


(ii) What is the function of an amplifier?


(iii) Which basic electronic device is used in the amplifier?


 25

A 2 μF capacitor, 100 W resistor and 8 H inductor is connected in series with an AC source.

(i) What should be the frequency of the source such that current drawn in the circuit is maximum? What is this frequency called?


(ii) If the peak value of e.m.f. of the source is 200 V, find the maximum current.


(iii) Draw a graph showing variation of amplitude of circuit current with changing frequency of applied voltage in a series LRC circuit for two different values of resistance R1 and R2 (R1 > R2).


(iv) Define the term ‘Sharpness of Resonance’. Under what condition, does a circuit. become more selective?


OR


(i) With the help of a neat and labelled diagram, explain the principle and working of a moving coil galvanometer.


(ii) What is the function of uniform radial field and how is it produced?


(iii) Define current sensitivity of a galvanometer. How is current sensitivity increased?


 26

(i) In the circuit diagram given below, AB is a uniform wire of resistance 15 Ω and length 1 m. It is connected to a cell E1 of emf 2V and negligible internal resistance and a resistance R. The balance point with another cell E2 of emf 75 mV is found at 30 cm from end A. Calculate the value of R.


(ii) Why is potentiometer preferred over a voltmeter for comparison of emf. of cells?


(iii) Draw a circuit diagram to determine internal resistance of a cell in the laboratory.


OR


(i) Plot a graph showing variation of voltage vs the current drawn from the cell.


How can one get information from this plot about the emf of the cell and its internal resistance?


(ii) Two cells of emf’s E1 and E2 and internal resistance r1 and r2 are connected in parallel. Obtain the expression for the emf and internal resistance of a single equivalent cell that can replace this combination?