Interference Of Waves (Board Level)

1.

Light waves each of amplitude ‘a’ and frequency \displaystyle \omega emanating from two coherent light sources superpose at a point.  If the displacements due to these waves are given by \displaystyle {{y}_{1}}=a\,\cos \,\omega tand \displaystyle {{y}_{2}}=a\,\cos \,\left( {\omega t+\phi } \right), where \displaystyle \phi is the phase difference between the two, obtain the expression for the resultant intensity at the point.

2.

What is the relation between path difference and wavelength for constructive interference of two waves?

3.

What is the relation between path difference and wavelength for destructive interference?

4.

What happens to the interference pattern if phase difference between two light sources varies continuously?

5.

Explain the statement, ‘light added to light can produce darkness’.

6.

When a low flying aircraft passes overhead, we sometimes notice a slight shakingof the                picture on our TV screen. Suggest a possible explanation.

7.

When monochromatic light travels from one medium to another its wavelength changes but frequency remains the same.  Explain.

 8

(a) The refractive index of glass is 1.5. What is the speed of light in glass? (Speed of light in vacuum is 3.0 × 10⁸ m s^–1)

(b)    Is the speed of light in glass independent of the colour of light? If not, which of the  two

9.

Out of speed, frequency and wavelength, name the parameter(s) which remain the same on reflection.

10.

What is the ratio of slit widths when amplitudes of light ways from them have ratio \displaystyle \sqrt{3}\,\,:\,\,\sqrt{2}?

11.

The refractive index of glass is 1.5 for light wave of \displaystyle \lambda =6000\,{\AA} in vacuum.  Calculate their wave length in glass.

12.

Calculate time taken by light to travel 1 cm thickness of glass of \displaystyle \mu =1.5.

13.

What are the essential conditions for two light waves to be coherent?

14.

Let us list some of the factors, which could possibly influence the speed of wave propagation:

 (i)   nature of the source.

(ii)   direction of propagation.

 (iii)  motion of the source and/or observer.

 (iv)  wavelength.

 (v)  intensity of the wave.

On which of these factors, if any, does

 (a) the speed of light in vacuum,

 (b) the speed of light in a medium (say, glass or water),  depend?

15.

What are coherent sources of light? Why are coherent sources required to obtained sustained interference pattern?

16.

What is meant by interference of light? Describe briefly Young’s double slit experiment to demonstrate interference of light.

17.

Derive the conditions for constructive and destructive interference.