Questions: A light ray passes from air (refractive index n1=1.00) into another material. The angle of incidence is 30°, and the angle of refraction is 20°. Using Snell's Law: n1 sin(theta1)=n2 sin(theta2) calculate the refractive index of the second material (n2), and identify the material from the following options: Quartz (n=1.46) Diamond (n=2.42) Water (n=1.33) Crown Glass (n=1.52) Quartz Water Diamond Crown Glass

$A light ray passes from air (refractive index n1=1.00) into another material. The angle of incidence is 30°, and the angle of refraction is 20°. Using Snell's Law: n1 sin(theta1)=n2 sin(theta2) calculate the refractive index of the second material (n2), and identify the material from the following options: Quartz (n=1.46) Diamond (n=2.42) Water (n=1.33) Crown Glass (n=1.52) Quartz Water Diamond Crown Glass$

Transcript text: A light ray passes from air (refractive index $\mathbf{n} \_1=1.00 \mathrm{n} 1=1.00$ ) into another material. The angle of incidence is $30^{\circ}$, and the angle of refraction is $20^{\circ}$. Using Snell's Law: \[ n_{1} \sin \left(\theta_{1}\right)=n_{2} \sin \left(\theta_{2}\right) \] calculate the refractive index of the second material $\left(n_{2}\right)$, and identify the material from the following options: \begin{tabular}{|l|l|} \hline Quartz $(\mathrm{n}=1.46)$ & Diamond $(\mathrm{n}=2.42)$ \\ \hline Water $(\mathrm{n}=1.33)$ & Crown Glass $(\mathrm{n}=1.52)$ \\ \hline \end{tabular} Quartz Water Diamond Crown Glass

Solution

Solution Steps

Step 1: Apply Snell's Law

Use Snell's Law to relate the angles and refractive indices: \[ n_{1} \sin \left(\theta_{1}\right) = n_{2} \sin \left(\theta_{2}\right) \] Substitute the known values: \[ 1.00 \times \sin(30^{\circ}) = n_{2} \times \sin(20^{\circ}) \]

Step 2: Calculate $\sin(30^{\circ})$ and $\sin(20^{\circ})$

Calculate the sine of the given angles: \[ \sin(30^{\circ}) = 0.5 \] \[ \sin(20^{\circ}) \approx 0.342 \]

Step 3: Solve for $n_{2}$

Rearrange the equation to solve for $n_{2}$: \[ n_{2} = \frac{1.00 \times 0.5}{0.342} \] Calculate $n_{2}$: \[ n_{2} \approx 1.46 \]

Step 4: Identify the Material

Compare the calculated refractive index with the given options: