4th order dark fringe and 2nd order bright fringe spaced 2.5 cm aparte appear on the screen placed 1 m behind the double slit. What is the spacing of the slits if the wavelegth ofincident light is 500nm?
First I converted the numbers:
x= .025m
wavelength= 5x10^-7m
L=1m
d=?
I used d= wavelenght*L/x and got 2x10^-5 m
but I got this problem wrong and I was wondering how you would correctly solve this problem. Did I assign the correct numbers with the correct letters?
Yes, you assigned the correct numbers to the corresponding variables for the given problem. However, there seems to be a slight mistake in the calculation.
Let's go through the steps again to solve the problem correctly.
Given:
x = 0.025 m (distance between the 4th order dark fringe and the 2nd order bright fringe)
wavelength = 5 x 10^-7 m (wavelength of incident light)
L = 1 m (distance between the double slit and the screen)
d = ? (spacing between the slits)
To find the spacing between the slits (d), we can use the formula:
x = (wavelength * L) / d
Rearranging the equation:
d = (wavelength * L) / x
Now, substitute the given values into the equation:
d = (5 x 10^-7 m) * (1 m) / (0.025 m)
Calculating this expression will give us the correct answer:
d = 2 x 10^-5 m
Hence, the correct spacing between the slits is 2 x 10^-5 m.