Question

Why the fringes are of equal width?

Answer 1

Hint: Interference pattern can be observed when coherent light from two sources like double slit of YDSE interfere on screen.On screen alternate high intensity strip and low intensity strip can be seen, high intensity strip is called as bright fringe and low intensity is called as dark fringe. Difference between two consecutive dark fringes is called as fringe width. Check for the relationship between width of fringe and it’s dependency on position.

Complete answer:
Young’s double-slit experiment uses two coherent sources of light placed at a small distance apart, usually, only orders of magnitude greater than the wavelength of light is used. YDSE experiment helped in understanding the wave theory of light. A screen is placed at a large distance ’D’ away from the slits.

In Young's double slit experiment, position of ${n^{th}}$ order bright fringe is given by:
${y_n} = \dfrac{{nD\lambda }}{d}$
Where:
n represents the ${n^{th}}$ bright fringe
λ is the wavelength of light used
d is the width of the slit
D is the distance between light source and slit

Thus, the fringe width of bright fringe ${y_{n + 1}} - {y_n} = \dfrac{{D\lambda }}{d}$ which is independent from the position n.

Similarly for dark fringe, position ${m^{th}}$ order fringe is given by:
${y_m} = (m + \dfrac{1}{2})\dfrac{{D\lambda }}{d}$

Thus, the fringe width of dark fringe ${y_{m + 1}} - {y_m} = \dfrac{{D\lambda }}{d}$ which is independent from the position m.

Note: In Young’s double-slit experiment the width of the fringe is independent of the fringe position and only depends on wavelength, distance and width of slit.Also If white light is used in place of monochromatic light, then coloured fringes are obtained on the screen with red fringes larger in size than violet.