The Holographic Security Sticker · AI Generator #GEN-014B31E5

Physics · optics

Problem

A holographic security sticker on a credit card creates rainbow colors through diffraction. The sticker contains parallel grooves with spacing d=1.2  μmd = 1.2\;\mu\text{m}. When white light hits the sticker at normal incidence, you observe the first-order diffracted red light (λ=650  nm\lambda = 650\;\text{nm}) at angle θr\theta_r from the normal, and first-order diffracted blue light (λ=450  nm\lambda = 450\;\text{nm}) at angle θb\theta_b from the normal. You then tilt the card so that light hits the sticker at an incident angle of 30°30° from the normal. At what angle from the normal will you now observe the first-order diffracted red light? Assume the diffraction occurs on the same side of the normal as the incident light.

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