Question

In a ray of light travels from air to water, the ratio between $$\sin i$$ and $$\sin r$$ is denoted by $${}^{a}\mu_{w}$$. However, when the ray of light emerges from water to air the ratio of $$\sin i$$ and $$\sin r$$ is denoted by $${}^{w}\mu_{a}$$. The relation between $${}^{a}\mu_{w}$$ and $${}^{w}\mu_{a}$$ is:

Options

• $$^{a}\mu_{w} = \dfrac{1}{{}^{w}\mu_{a}}$$

• $$\dfrac{{}^{a}\mu_{w}}{{}^{w}\mu_{a}} = 1$$

• $$^{a}\mu_{w} \times {}^{w}\mu_{a} = 1$$

• both $$^{a}\mu_{w} = \dfrac{1}{{}^{w}\mu_{a}}$$ and $$^{a}\mu_{w} \times {}^{w}\mu_{a} = 1$$

Answer 1

Both $$^{a}\mu_{w} = \dfrac{1}{{}^{w}\mu_{a}}$$ and $$^{a}\mu_{w} \times {}^{w}\mu_{a} = 1$$

Explanation:

The refractive indices for the two opposite directions are reciprocals:

$$^{a}\mu_{w} = \dfrac{1}{{}^{w}\mu_{a}}$$

This is equivalent to saying that their product is 1.