Question

(a) If the first-order maximum for pure-wavelength light falling on a double slit is at an angle of 10.0º, at what angle is the second-order maximum?
(b) What is the angle of the first minimum?
(c) What is the highest-order maximum possible here?

Answer 1

(a)y(max) = 2k Lλ/2d = k Lλ/d
tan φ= k Lλ/L d = k λ/d
tan φ₁=1•λ/d
tanφ₂=2•λ/d
tan φ₂=2•tan φ₁ 2•tan10
φ₂ ≃20⁰
(b) y(min) = (2k+1) Lλ/2d
tan φ = (2k+1) Lλ/2Ld =(2k+1) λ/2d
tan φ₋₁=λ/2d = tan φ₁/2 =tan10/2
φ₋₁ ≃5⁰
(c)tan φ₁=1•λ/d
Max wavelength of visual range id λ= 0.76•10⁻⁶ m λ(max)
d= λ/tan φ₁= 0.76•10⁻⁶/tan10=4.3•10⁻⁶ m
k=d sinφ/ λ
sinφ≤1 . Take sinφ=1
k= 4.3•10⁻⁶/0.76•10⁻⁶=5.67.
k(max) = 5