Final answer:
To determine the incident angle for 470 nm light in flint glass to achieve the same refraction angle as 610 nm light in fused quartz, we apply Snell's law. By calculating the refractive angle in fused quartz first, we can solve for the incident angle in flint glass using its index of refraction for the 470 nm light, which must be provided for a complete solution.
Step-by-step explanation:
To find out at what incident angle 470 nm light must enter flint glass to have the same angle of refraction as a 610 nm light ray entering fused quartz at a 55.0º angle, we can use Snell's law. Snell's law states that n1 * sin(θ1) = n2 * sin(θ2), where n1 and n2 are the refractive indices of the first and second mediums respectively, and θ1 and θ2 are the incident and refracted angles respectively.
To find the angle of refraction in fused quartz, we can rearrange Snell's law with the given values (assuming air's refractive index to be approximately 1): sin(θ2) = sin(55.0º) / 1.544 (fused quartz's refractive index). Once we have θ2, we can use it with flint glass's refractive index to determine the necessary incident angle θ1 for 470 nm light (the refractive index for flint glass at this wavelength would need to be known).
Unfortunately, without the respective refractive indexes for 610 nm and 470 nm light in flint glass, we cannot complete the calculation. However, the general process involves calculating the angle of refraction in fused quartz and then using that angle to find the incident angle in flint glass with the refractive index for 470 nm light.