Physics
Physics
Problem
A stack of two transparent dielectric layers is deposited on glass (). The top layer has index and thickness . Directly beneath it is layer with index and thickness . Monochromatic light of wavelength in air is incident normally on the stack. Which statement best describes the reflected intensity at wavelength compared to that from bare glass? a) Reflection is increased because the two phase reversals make the reflected waves add in phase. b) Reflection is greatly reduced because the first two reflected waves cancel each other. c) Reflection is essentially unchanged because additional reflections from the lower interfaces exactly compensate any reduction. d) Reflection is increased only for wavelengths shorter than and decreased for longer wavelengths.Intuitive explanation
This is a thin-film interference problem where two quarter-wave coatings work together to control reflection. The key is tracking how light reflects at each interface and whether those reflections interfere constructively or destructively. Since each layer is exactly one quarter wavelength thick (in its own medium), the phase shift accumulated in each layer is —this determines whether reflections add or cancel. You'll need to compare the refractive indices at each interface to predict whether the net reflected wave is enhanced or suppressed relative to bare glass.
Intuitive explanation
This is a thin-film interference problem where two quarter-wave coatings work together to control reflection. The key is tracking how light reflects at each interface and whether those reflections interfere constructively or destructively. Since each layer is exactly one quarter wavelength thick (in its own medium), the phase shift accumulated in each layer is —this determines whether reflections add or cancel. You'll need to compare the refractive indices at each interface to predict whether the net reflected wave is enhanced or suppressed relative to bare glass.