The Rainbow Prism Clock · AI Generator #GEN-E47929A1

Physics · optics

Problem

A glass prism with apex angle A=60°A = 60° and refractive index n=1.5n = 1.5 is mounted on a rotating turntable. White light from a distant source enters one face of the prism and emerges from the other face, creating a spectrum on a screen 2.0  m2.0\;\text{m} away. As the turntable slowly rotates, there is a specific orientation where the red light (λ=700  nm\lambda = 700\;\text{nm}) emerges at minimum deviation. At this same orientation, blue light (λ=450  nm\lambda = 450\;\text{nm}) emerges at a different angle due to dispersion. The refractive index varies with wavelength according to n(λ)=1.48+2.1×104λ2n(\lambda) = 1.48 + \frac{2.1 \times 10^4}{\lambda^2} where λ\lambda is in nanometers. When the red light is at minimum deviation, what is the separation distance between the red and blue spots on the screen?

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