An optical two-slit experiment is setup with its slits separated by 48 X 10-3 cm

Question

An optical two-slit experiment is setup with its slits separated by 48 X 10-3 cm and produces a second order maximum at an angle of 0.09o.

a) What is the wavelength of light used in this experiment? 377Nm OK

b) What would the wavelength of the light need to be if we kept the position of the second order maximum the same, but increased the slit separation of 69 X 10-3 cm?
I got 542Nm it says no. Why???? What did i do wrong?

Appreciate any help thanks!!!!

i used the formula d=m times lambda/ sin (theta) for first equation and it worked, why isn't it working on the second one??

Explanation / Answer

yes part a is 377 nm


part b
given
d = 0.0069 m
m = 2
theta = ?

ym = R m/d

y2 / R = 2 (377x10-9 m)/0.0048 m = 1.57 x10-3

and

y2/R stays the same

solve for

ym = R m/d

= (ym/R) d / m

= (0.0069m)(1.57x10-3)/2

= 542 nm

hmmmm

try

= d sin / m

= (0.0069 m) sin0.09 / 2

= 542 nm

for this method Iwould expect to have changed that's why I did it the other way first

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