A Larger Change in Direction

Again the index of refraction for air is taken to be $n_1=1\text{.}\text{00}$, and we are given ${\theta }_1=\text{30}\text{.}\mathrm{0º}$. We can look up the index of refraction for diamond in Table 25.1, finding $n_2=2\text{.}\text{419}$. The only unknown in Snell’s law is ${\theta }_2$, which we wish to determine.

Solving Snell’s law for sin ${\theta }_2$ yields

Entering known values,

The angle is thus

For the same $\mathrm{30º}$ angle of incidence, the angle of refraction in diamond is significantly smaller than in water ($\mathrm{11.9º}$ rather than $\mathrm{22º}$—see the preceding example). This means there is a larger change in direction in diamond. The cause of a large change in direction is a large change in the index of refraction (or speed). In general, the larger the change in speed, the greater the effect on the direction of the ray.