Question

For which colour is the fringe width minimum?
A. Violet
B. Red
C. Green
D. yellow

Answer 1

Hint: The above problem can be resolved by applying the mathematical formula relating to the light rays' fringe width and light rays' wavelength. Moreover, the fringe width always varies directly with the wavelength of light as per the mathematical relation. And the light ray possessing the maximum value of wavelength will have a value of fringe width to be more generous.


Complete step by step answer
The fringe width of any colour is related to the wavelength of light having specific colour. The mathematical relation for the fringe width \[\left( \beta \right)\] and the wavelength \[\left( \lambda \right)\] is given as,
\[\beta = \lambda \left( {\dfrac{D}{d}} \right)................\left( 1 \right)\]
Here, D is the distance between the slit and the screen and d is the distance between the slits.
From equation 1, it is clear that the fringe varies directly with the wavelength of the light involving the colour. The wavelength of the Red light is minimum and the wavelength of violet light is maximum.
 Therefore, the fringe width for the violet light is maximum and option A is correct.


Note: Try to understand the fringe width and factors that can affect the value of the fringe width. The Fringe width generally depends on the distance between the slit and the distance from the screen. Along with these variables, the fringe width also depends on the wavelength formed by the light rays. Hence, the longer the wave, the fringe width will be maximum, and the shorter the wave, the minimum fringe width will be observed.