for the refractive index of the slab material. We are given the angle of incidence (i) and the angle of refraction (r). We assume the light is entering the slab from air, so the refractive index o
This physics problem tests your understanding of fundamental physical laws and their applications. The step-by-step solution below breaks down the problem using relevant equations and physical reasoning.
ScanSolve AI Answer
Step 1: Identify the given values and the formula.
The problem asks for the refractive index of the slab material. We are given the angle of incidence ($i$) and the angle of refraction ($r$). We assume the light is entering the slab from air, so the refractive index of the first medium (air) is $n_1 = 1$.
Given:
Angle of incidence, $i = 40^\circ$
Angle of refraction, $r = 26^\circ$
Refractive index of air, $n_1 = 1$
We use Snell's Law:
$$n_1 \sin(i) = n_2 \sin(r)$$
where $n_2$ is the refractive index of the slab material.
Step 2: Substitute the given values into Snell's Law.
$$1 \cdot \sin(40^\circ) = n_2 \sin(26^\circ)$$
Step 3: Calculate the sine values.
$$\sin(40^\circ) \approx 0.6428$$
$$\sin(26^\circ) \approx 0.4384$$
Step 4: Solve for $n_2$.
$$0.6428 = n_2 \cdot 0.4384$$
$$n_2 = \frac{0.6428}{0.4384}$$
Step 5: Perform the division.
$$n_2 \approx 1.4663$$
Step 6: Round the result to an appropriate number of significant figures.
$$n_2 \approx 1.47$$
The refractive index of the slab material is $\boxed{\text{1.47}}$.
