A film of index of refraction n₁ coats a surface with index of refraction n₂.When n₁ n₂,the condition for constructive interference for reflected monochromatic light of wavelength $\lambda$ in air is A) $t = m \frac { \lambda } { n _ { 1 } }$ . B) $t = \left( m + \frac { 1 } { 2 } \right) \frac { \lambda } { n _ { 1 } }$ . C) $2 t = m \frac { \lambda } { n _ { 1 } }$ . D) $2 t = \left( m + \frac { 1 } { 2 } \right) \frac { \lambda } { n _ { 1 } }$ . E) $4 t = m \frac { \lambda } { n _ { 1 } }$ .

Question

A film of index of refraction n₁ coats a surface with index of refraction n₂.When n₁ > n₂,the condition for constructive interference for reflected monochromatic light of wavelength $\lambda$ in air is A) $t = m \frac { \lambda } { n _ { 1 } }$ . B) $t = \left( m + \frac { 1 } { 2 } \right) \frac { \lambda } { n _ { 1 } }$ . C) $2 t = m \frac { \lambda } { n _ { 1 } }$ . D) $2 t = \left( m + \frac { 1 } { 2 } \right) \frac { \lambda } { n _ { 1 } }$ . E) $4 t = m \frac { \lambda } { n _ { 1 } }$ .

Quizplus · Accepted Answer

When n1 > n2, a phase shift of π occurs upon reflection at the first boundary, requiring an additional half-wavelength path difference for constructive interference.

A Film of Index of Refraction N1 Coats a Surface λ\lambdaλ

A Film of Index of Refraction N₁ Coats a Surface $\lambda$