Answer:
the refractive index of the liquid is 2.08
Explanation:
The diffraction formula is:
d sin(θ) = mλ
where
Thus,
d sin(θ₁) = m λ₁ (1) and
d sin(θ₂) = m λ₂ (2)
Dividing equation (1) by equation (2) you get
sin(θ₁) / sin(θ₂) = λ₁ / λ₂ (3)
λ can be expressed as
λ = v / f
where
Therefore,
λ₁ = v₁ / f
λ₂ = v₂ / f
Thus,
λ₁ / λ₂ = v₁ / v₂
Therefore, substituting the above expression for λ₁ / λ₂ into equation (3), we get
sin(θ₁) / sin(θ₂) = v₁ / v₂
where
The expression for the refractive index is
n = c / v , which can also be expressed as
n = v₁ / v₂
Therefore,
n = sin(θ₁) / sin(θ₂)
n = sin(38.2°) / sin(17.3°)
n = 2.08
Therefore, the refractive index of the liquid is 2.08
