an incident ray of light strikes a diamond at an angle of 45°. the index of refraction of air is 1.0003 and…

Explanation:

Step1: Recall Snell's Law

$n_1\sin\theta_1 = n_2\sin\theta_2$ where $n_1$ is the index of refraction of the incident - medium, $\theta_1$ is the angle of incidence, $n_2$ is the index of refraction of the refracting - medium, and $\theta_2$ is the angle of refraction.

Step2: Identify the given values

$n_1 = 1.0003$, $\theta_1=45^{\circ}$, $n_2 = 2.42$.

Step3: Substitute the values into Snell's Law

$1.0003\times\sin45^{\circ}=2.42\times\sin\theta_2$ Since $\sin45^{\circ}=\frac{\sqrt{2}}{2}\approx0.707$, we have $1.0003\times0.707 = 2.42\times\sin\theta_2$. $0.7072121=2.42\times\sin\theta_2$.

Step4: Solve for $\sin\theta_2$

$\sin\theta_2=\frac{0.7072121}{2.42}\approx0.292236$.

Step5: Find $\theta_2$

$\theta_2=\sin^{- 1}(0.292236)\approx17^{\circ}$.

Answer:

$17^{\circ}$