A single-layer antireflection coating is applied to the outer surface of a glass cover plate that protects a silicon solar cell. The arrangement, from top (incident side) to bottom, is air (n0=1.00) → coating (n1=1.38) → glass (n2=1.50) → silicon (n3=3.50).
Sunlight is assumed to arrive at normal incidence, but the designer wishes to minimize reflection specifically at wavelength λ0=550nm in air.
(a) For each of the three interfaces (air–coating, coating–glass, and glass–silicon), indicate whether a reflected ray experiences a half-wavelength phase change. Explain your reasoning for each interface.
(b) Considering only the first two reflected rays (from the air–coating and coating–glass interfaces), derive an expression for the coating thickness d that gives minimum reflected intensity at wavelength λ0 for normal incidence.
(c) Using λ0=550nm and n1=1.38, calculate the smallest non-zero thickness dmin that satisfies the condition derived in part (b). Express your answer to the nearest nanometer.
(d) Discuss qualitatively why adding the reflection from the glass–silicon interface does not substantially alter the thickness found in part (c) for the purpose of reducing the net reflected power.