Asingle slit diffraction experiment performed with an argon laser of wavelength 454.6 nm produces a pattern on a screen with dark fringes (minima) separated by 10 mm. if we replace the slit with another slit of double the width of the original one, without changing anything else in the setup, what will be the new separation between dark fringes?

5mm

Step-by-step explanation:

The formula of the separation between fringes is given by

d = λD/a where d is the separation between fringes, λ is the wavelenth and a is the slit width. If nothing but the slit width is the changed and the setup is unchanged then we can write a comparitive equation such as below

(d2/d1) = (λD/a2)/(λD/a1)

We know that the new slit is double the width, which means a2 = 2 x a1

Substituting the values and simplifying the above equation becomes

(d2/d1) = (λD/2.a1)/(λD/a1) = (λD/2.a1) x (a1/λD/a1)

(d2/d1) = 1/2

d2/10 = 1/2

d2 = 5mm

I don't understand. Maybe you could state it more clearly instead of copy pasting?