Answer:
θ = 34.77°
Explanation:
From diffraction equation:
[tex]m\lambda = dSin\theta[/tex]
where,
m = order of diffraction
λ = wavelength of light used
d = slit separation
θ = angle
Therefore, for initial case:
m = 2
λ = 600 nm = 6 x 10⁻⁷ m
d = slit seperation = ?
θ = angle 20°
Therefore,
[tex](2)(6\ x\ 10^{-7}\ m)=d(Sin\ 20^o)\\\\d = \frac{12\ x 10^{-7}\ m}{0.342}\\\\d = 3.5\ x\ 10^{-6}\ m[/tex]
Now, for the second case:
m = 5
λ = 600 nm = 6 x 10⁻⁷ m
d = slit seperation = (1.5)(3.5 x 10⁻⁶ m) = 5.26 x 10⁻⁶ m
θ = angle = ?
Therefore,
[tex](5)(6\ x\ 10^{-6}\ m) = (5.26\ x\ 10^{-6}\ m)Sin\theta\\\\Sin\theta = \frac{(5)(6\ x\ 10^{-7}\ m)}{(5.26\ x\ 10^{-6}\ m)}\\\\\theta = Sin^{-1}(0.5703)[/tex]
θ = 34.77°
