Physics
posted by Angel .
Light falls on a double slit with slit separation
of 2.19 × 10
−6 m, and the ﬁrst bright fringe is
seen at an angle of 12.7
◦
relative to the central
maximum.
What is the wavelength of the light?
Answer in units of nm

λ = d• tanα = 2.19•10^6 • 0.225 =4.94 •10^7 m = 494 nm

It says incorrect. Can you explain the process?

The coordinate of the kmaximum (separation between the central and the first maxima) is
x(max) = k•λ•L/d,
where L is the separation between the slits and the screen, d is the separation between the slits.
Now, imagine the triangle : the midpoint between slits (taking into account that the slits are very close to each other, this point is the slit), the central maximum on the screen, and the first bright fringe. In this triangle
tan α = x(1max)/L
x(1max) = L •tan α
Then for k=1
x(1max) = λ•L/d,
L •tan α =λ•L/d,
tan α = λ/d,