Question

What will be the effect on interference fringes if red light is replaced by blue light?

Answer 1

In this question we have to tell whether the effect on interference fringes when color of light is changed because every color have different wavelength and for different wavelength we get some changes on the pattern of interference on the screen here two colors are given we have to compare both the wavelength and find the result.

Complete step by step solution:
In young’s experiment when slits are placed close to each other, an interference pattern is shown on the screen having alternate bright and dark fringes and these fringes have equal width which is directly proportional to wavelength of light and also distance between slit and screen while inversely proportional to the distance between the slits as shown in below expression:-
$\beta =\dfrac{D\lambda }{d}$
Where
$D=$ distance between the screen and slit.
$d=$Distance between the two slits.
In this question we have to tell the effect on interference pattern when red light is replaced by blue light for that we will use the fringe width formula of interference which can be expressed mathematically as $\beta =\dfrac{D\lambda }{d}$.
Since here red light is replaced by blue light as we also know that different colors have different wavelengths.
Since we know that the wavelength of blue light is least while wavelength of red light is maximum.
Which can expressed mathematically as,
${{\lambda }_{red}}>{{\lambda }_{blue}}$
Since Fringe width and wavelength are directly proportional to each other according to above formula than if wavelength of red light is maximum then fringe width made by red light is also maximum which means fringes will bar from each other and wavelength of blue is least so fringe width made by blue light is also least which means they becomes close to each other.
So mathematically it can be represented as,
${{\beta }_{red}}>{{\beta }_{blue}}$
So we can conclude that if red light is replaced by blue light then the width of interference fringes decreases which means fringes come closer to each other.

Note: Interference pattern can only be observed when two coherent sources are used , coherent sources are those sources which have same frequency and constant or zero phase difference for sustained interference pattern we have to take two sources of same amplitude so that we get perfect contrast in bright and dark fringes.