Question

Two narrow slits are 0.12 mm apart. Light of wavelength 550 nm illuminates the slits, causing an interference pattern on a screen 1.0 m away. Light from each slittravels to the m=1 maximum on the right side of the central maximum. How much farther did the light from the left slit travel than the light from the right slit?(answer in nm)

Answer 1

d_L = distance traveled by light from left slit

d_R = distance traveled by light from right slit

$\Delta$x = path difference = d_L - d_R

m = 1

$\lambda$ = wavelength = 550 nm

Path difference is given as

$\Delta$x = m $\lambda$

inserting the values

d_L - d_R = 1 x 550

d_L - d_R = 550 nm

Answer 2

For a double slit interference experiment, the path difference i.e. how much farther one light beam travels than the other) is an integer number of wavelengths. So the path difference for the first interference max is one wavelength, the path difference to the second maximum is two wavelengths, etc etc. For this problem, the path difference of the first maximum i:s Path difference-mx Wave length Path difference 1x550 Path difference 550

Answer 3

the path difference between the two lights should be an integral multiple of wavelength

$\delta x =n\lambda$

for first maxima n =1

hence the path difference = wavelength = 550nm