## Monochromatic coherent light shines through a pair of slits. If the wavelength of the light is decreased, which of the following statements

Question

Monochromatic coherent light shines through a pair of slits. If the wavelength of the light is decreased, which of the following statements are true of the resulting interference pattern? (There could be more than one correct choice.)
a. The distance between the maxima decreases.
b. The distance between the minima decreases.
c. The distance between the maxima stays the same.
d. The distance between the minima increases.
e. The distance between the minima stays the same.

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5 months 2021-08-19T05:32:24+00:00 1 Answers 24 views 0

he correct answers are a, b

Explanation:

In the two-slit interference phenomenon, the expression for interference is

d sin θ= m λ                       constructive interference

d sin θ = (m + ½) λ             destructive interference

in general this phenomenon occurs for small angles, for which we can write

tanθ = y / L

tan te = sin tea / cos tea = sin tea

sin θ = y / La

un

derestimate the first two equations.

Let’s do the calculation for constructive interference

d y / L = m λ

the distance between maximum clos is and

y = (me / d) λ

this is the position of each maximum, the distance between two consecutive maximums

y₂-y₁ = (L   2/d) λ – (L 1 / d) λ₁          y₂ -y₁ = L / d λ

examining this equation if the wavelength decreases the value of y also decreases

the same calculation for destructive interference

d y / L = (m + ½) κ

y = [(m + ½) L / d] λ

again when it decreases the decrease the distance

the correct answers are a, b