Problem 8: Consider the sodium doublet vapor lines, which have wavelengths of 58

Question

Problem 8: Consider the sodium doublet vapor lines, which have wavelengths of 589 nm (line a) and 589.6 nm (line b) Randomized Variables w=2.15 m L - 1.05 m Part (a) Find the angle (in degrees)between the first minima for the two sodium vapor lines, when they fall upon a single slit with a width o 2.15 m. Numeric : A numeric value is expected and not an expression. Part (b) What is the distance in mm between these minima if the diffraction pattern falls on a screen 1.05 m from the slit? Numeric : A numeric value is expected and not an expression.

Explanation / Answer

(A) for nth minima,

sin(theta_n) = (n - 0.5) lambda / d

sin(theta1) = 0.5 x 589 x 10^-9 / 2.15 x 10^-6 = 0.137

theta_a = 7.87deg

sin(theta_b) = 0.5 x 589.6 x 10^-9 / 2.15 x 10^-6

theta_b = 7.88 deg

delta(theta) = 0.011 deg

(b) y = (n - 0.5) lambda D / d

delta(y) = 0.5 x 0.6 x 10^-9 x 1.05 / (2.15 x 10^-6)

= 1.465 x 10^-4 m

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