Q10 · Wave Optics

Problem

Young’s double slit with green, red, blue light separately. Order fringe widths β_G, β_R, β_B.

Options

Option	Value
(A)	β_G > β_B > β_R
(B)	β_B > β_G > β_R
(C)	β_R > β_B > β_G
(D)	β_R > β_G > β_B

Key insight: Fringe width β = λD/d — directly proportional to wavelength.

Setup

flowchart LR
  L["β = λD/d"] --> R["Red: largest λ → widest β"]
  L --> G["Green: medium β"]
  L --> B["Blue: smallest λ → narrowest β"]

1. Fringe formula

β proportional to λ.

$$\beta = \frac{\lambda D}{d}$$

2. Order wavelengths

λ_R > λ_G > λ_B.

$$\beta_R > \beta_G > \beta_B \Rightarrow (D)$$

Deep dive

Young’s double slit: β = λD/d. Red (λ ≈ 650 nm) > green (550 nm) > blue (450 nm), so β_R > β_G > β_B.

Common pitfalls

• Reversing the order
• Thinking all colors give same β for fixed setup

Hints

• β = λD/d — larger λ gives wider fringes.

Answer

(D)