4th order dark fringe and 2nd order bright fring spaced 2.5cm apart appear on the screen placed 1 m behind the double slit. What is the spacing of the slits if the waveleght of incident light is 500nm?
x=2.5cm=.025m
L=1m
wavelegth= 500nm = 5x10^-7m
d=?
x/L=wavelength/d
d= (wavelegth)(L)/x
=5x10^-7m*1m/ .025
= 2x10^-5m
Is this correct?
Yes, your calculation is correct. The formula you used is the correct formula for calculating the spacing between the double slits. The formula is:
x / L = λ / d,
where x is the distance between the fringes on the screen (2.5 cm = 0.025 m in this case), L is the distance between the double slit and the screen (1 m in this case), λ is the wavelength of the incident light (500 nm = 5 × 10^-7 m in this case), and d is the spacing between the double slits (which is what we want to calculate).
Rearranging the formula, we get:
d = (λ × L) / x = (5 × 10^-7 m) × (1 m) / (0.025 m) = 2 × 10^-5 m.
So, the spacing of the slits is 2 × 10^-5 m.