The refractive index for light traveling from air to Lucite is _____, and from Lucite to air the refractive index is_________________. How are these two values related?
The Correct Answer and Explanation is:
Let us answer the question directly:
The refractive index for light traveling from air to Lucite is approximately 1.50.
The refractive index for light traveling from Lucite to air is approximately 0.67.
Relationship between the two values:
The two values are reciprocals of each other. If the refractive index from air to Lucite is nair→Luciten_{air \rightarrow Lucite}nair→Lucite, then the refractive index from Lucite to air is 1nair→Lucite\frac{1}{n_{air \rightarrow Lucite}}nair→Lucite1. In this case, 11.50≈0.67\frac{1}{1.50} \approx 0.671.501≈0.67.
Explanation:
Refractive index describes how much light bends when it moves from one medium to another. The refractive index nnn of a material is the ratio of the speed of light in a vacuum to the speed of light in that material. For air, the refractive index is approximately 1, since the speed of light in air is nearly equal to the speed of light in a vacuum. Lucite, which is a type of acrylic plastic, has a refractive index of about 1.50. This means that light slows down and bends as it enters Lucite from air.
When light travels from Lucite back into air, it speeds up. The refractive index for this transition is found by taking the reciprocal of the refractive index from air to Lucite. This reciprocal relationship occurs because the refractive index depends on the ratio of the speeds of light in the two media. Mathematically, if n1→2=v1v2n_{1 \rightarrow 2} = \frac{v_1}{v_2}n1→2=v2v1, then n2→1=v2v1n_{2 \rightarrow 1} = \frac{v_2}{v_1}n2→1=v1v2, which is the reciprocal.
This reciprocal relationship is essential in optics. It ensures that Snell’s Law, which governs the bending of light at an interface, remains consistent regardless of the direction the light is traveling.
