A pair of slits, separated by 0.185 mm, is illuminated by light having a wavelen

Question

A pair of slits, separated by 0.185 mm, is illuminated by light having a wavelength of ? = 610.0 nm. An interference pattern is observed on a screen 160 cm from the slits. Consider a point on the screen located at y = 2.00 cm from the central maximum of this pattern.

(a) What is the path difference ? for the two slits at the location y?
2.3 ?m

(b) Express this path difference in terms of the wavelength.
3.7
Your response is within 10% of the correct value. This may be due to roundoff error, or you could have a mistake in your calculation. Carry out all intermediate results to at least four-digit accuracy to minimize roundoff error. ?

I've got part (a) right, but I can't seem to get part (b). I've tried 3.7, 3.8, 3.77, 3.88 and they're all wrong. Any ideas on what I could be doing wrong? I'm calculating (2.3*10^-8)/(610*10^9)

Explanation / Answer

a) if d is the slit separation,

path diffrence = d*sin(theta)

from the figure, sin(theta) = opposite side/hypotenous

= 0.02/sqrt(0.02^2+1.6^2)

= 0.0125

so, path difference = 0.185*10^-3*0.0125

= 2.31*10^-6 m or 2.31 micro m

b) path diffrence = 2.31*10^-6*lamda/(610*10^-9)

= 3.78*lamda or 3.78 times of wavelength

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