Q25 of 26 Page 1

(i) In Young’s double slit experiment, deduce the condition for (a) constructive, and (b) destructive interference at a point on the screen. Draw a graph showing variation of intensity in the interference pattern against position ‘x’ on the screen.

(ii) Compare the interference pattern observed in Young’s double slit experiment with single slit diffraction pattern, pointing out three distinguishing features.


OR


(i) Plot a graph to show variation of the angle of deviation as a function of angle of incidence for light passing through a prism. Derive an expression for refractive index of the prism in terms of angle of minimum deviation and angle of prism.


(ii) What is dispersion of light? What is its cause?


(iii) A ray of light incident normally on one face of a right isosceles prism is totally reflected as shown in fig. What must be the minimum value of refractive index of glass? Give relevant calculations.



(i) Let us first explore the fringe width in Young’s Double slit experiment by drawing the double slit diagram.



The slit are at a distance of “d” from each other, the distance on the screen at point O to M is “x” and the distance between the screen and the slits is “D”. Now the intensity is maximum, at point M due to path difference, which is zero.


Let us denote the path difference as P


Therefore, the path difference is P = BO – AO = BO – CO = BC


In the right angle triangle of ABC, P =


(a) For Constructive Interference


Now it is considered that the path difference is equivalent to the integral multiple of wavelength ().



where


n is the number of fringes, λ is the wavelength, x is the distance from the middle of the screen to point O, D is the distance between the slits and the screen.


(b) For Destructive Interference


As for destructive interference, the distance (x) is



The graph showing variation of intensity in the interference pattern,


against position ‘x’ on the screen.



(ii) Comparing the interference pattern observed in Young’s double slit experiment with single slit diffraction pattern


1. The interference pattern have bright fringes with same intensity while vice versa is true for the diffraction pattern.


2. In interference pattern, the dark fringes have zero visibility while in diffraction pattern the dark fringes are easily prominent.


3. The widths of the fringes are same in single slit diffraction pattern as compared in interference pattern.


OR (i)


If the incidence angle is increased with time the deviation decreases to minimum deviation at a value of and then it increases again from the point of minimum deviation towards x-axis.



When the angle of deviation is at point “i” then


The refraction angles of the prism are


Now the refraction angle can be written in terms of angle of prism



If the angles of refraction are same then, the common angle of refraction is





Now finding the angle of incidence in term of prism angle is



Hence, the refractive index of the prism can be found out by the formula of Snell’s Law;




Therefore, the refractive index in terms of minimum deviation and angle of prism is



(ii)


The dispersion of the light is the splitting of the light ray into different colour mainly colour containing in the VIBGYOR. This dispersion happens because, the light beam carry wavelength of the different colour light, so when the light strikes the perfect angle it refracts into different colour at different position due to the change in wavelength.


(iii)


Let us see according to the diagram when the light ray falls on the point M of the surface AB it reflects out of the prism at from the surface CB. Therefore, the refractive index is calculated by



The angle C is the critical angle of the prism meaning the angle at which it will reflect perfectly at and out of the prism.


Let us take the angle C as, we have




Therefore, the minimum value of the refractive index of the glass is 1.41


More from this chapter

All 26 →
22

Draw a schematic ray diagram of reflecting telescope showing how rays coming from a distant object are received at the eye-piece. Write its two important advantages over a refracting telescope.

 23

Meeta’s father was driving her to the school. At the traffic signal she noticed that each traffic light was made of many tiny lights instead of a single bulb. When Meeta asked this question to her father, he explained the reason for this.

Answer the following questions based on above information:


(i) What were the values displayed by Meeta and her father?


(ii) What answer did Meeta’s father give?


(iii) What are the tiny lights in traffic signals called and how do these operate?


 24

(i) An a.c. source of voltage V = V0 sin ωt is connected to a series combination of L, C and R. Use the phasor diagram to obtain expressions for impedance of the circuit and phase angle between voltage and current. Find the condition when current will be in phase with the voltage. What is the circuit in this condition called?

(ii) In a series LR circuit XL = R and power factor of the circuit is P1. When capacitor with capacitance C such that XL = XC is put in series, the power factor becomes P2. Calculate P1/P2.


OR


(i) Write the function of a transformer. State its principle of working with the help of a diagram. Mention various energy losses in this device.


(ii) The primary coil of an ideal step up transformer has 100 turns and transformation ratio is also 100. The input voltage and power are respectively 220 V and 1100 W. Calculate


(a) Number of turns in secondary


(b) Current in primary


(c) Voltage across secondary


(d) Current in secondary


(e) power in secondary


 26

(i) Define the term drift velocity.

(ii) On the basis of electron drift, derive an expression for resistivity of a conductor in terms of number density of free electrons and relaxation time. On what factors does resistivity of a conductor depend?


(iii) Why alloys like constantan and manganin are used for making standard resistors?


OR


(i) State the principle of working of a potentiometer.


(ii) In the following potentiometer circuit AB is a uniform wire of length 1 m and resistance 10 Ω. Calculate the potential gradient along the wire and balance length AO ( = l).