A scientist shines a narrow beam of light from a block of transparent acrylic (index of refraction na=1.49) toward the flat acrylic–air boundary. The beam inside the acrylic makes an angle θ with the normal to the surface.
Parts (a)–(c) explore why some rays escape while others remain trapped inside the acrylic.
(a) Describe the physical condition that must be satisfied at the boundary for a ray to remain entirely inside the acrylic rather than refract into the air.
(b) Show qualitatively why the inequality na>nair is necessary for this trapping to occur, referring to the relative speeds of light in the two media.
(c) Infrared light typically has a larger wavelength in vacuum than visible light. If the dispersion of acrylic is such that its index decreases for longer wavelengths, explain whether the critical angle for infrared light at the acrylic–air boundary is larger, smaller, or the same as that for visible light. Justify your answer verbally without numerical calculation.