Suppose you illuminate two thin slits by monochromatic coherent light in air and find that they produce their first interference minima at / pm 35.09 degrees on either side of the central bright spot. You then immerse these slits in a transparent liquid and illuminate them with the same light. Now you find that the first minima occur at / pm 19.48 degrees instead. a) What is the index of refraction of this liquid?

n = 1,724

Explanation:

The interference pattern for two slits for the case of constructive interference is described by the expression

d sin θ = m λ

Where d is the separation of the slits, lm the wavelength and m an integer

When the slits are submerged the transparent liquid the wavelength of the light changes according to the relationship

λₙ = λ₀ / n

Where λ₀ is the wavelength in vacuum or air and n is the index of refraction of the material

Let's apply these relationships to our case, write the equations for the two situations

Air

d sin θ = m λ₀

Liquid

d sin θ₂ = m λₙ

d sin θ₂ = m λ₀ / n

Let's pass the variables to the left

sin θ = m λ₀ / d

n sin θ₂ = m λ₀ / d

Let's match the two equations

sin θ = n syn θ₂

n = sin θ / sin θ₂

Let's calculate

n = sin 35.09 / sin 19.48

n = 1,724