Question

A collimated light beam of intensity 𝐼₀ is incident normally on an air-dielectric (refractive index 2.0) interface. The intensity of the reflected light is _______𝐼₀. (Rounded off to two decimal places)

Answer 1

Correct Answer: 0.1

Given Data 

• Intensity of the incident light beam: \( I_0 \)
• Refractive index of the dielectric: \( n_2 = 2.0 \)
• Refractive index of air: \( n_1 = 1.0 \)

Step 1: Reflectance at an Air-Dielectric Interface

The reflectance \( R \) at an air-dielectric interface for normal incidence is given by:

\[ R = \left(\frac{n_2 - n_1}{n_2 + n_1}\right)^2 \]

Step 2: Substituting the Given Values

Substituting \( n_1 = 1.0 \) and \( n_2 = 2.0 \):

\[ R = \left(\frac{2.0 - 1.0}{2.0 + 1.0}\right)^2 \]

Step 3: Simplifying the Expression

\[ R = \left(\frac{1.0}{3.0}\right)^2 \]

\[ R = \frac{1.0}{9.0} \]

\[ R \approx 0.111 \]

Step 4: Calculating the Intensity of the Reflected Light

The intensity of the reflected light is given by:

\[ I_{\text{reflected}} = R \cdot I_0 \]

Step 5: Substituting the Reflectance Value

Using \( R \approx 0.111 \):

\[ I_{\text{reflected}} \approx 0.111 I_0 \]

Final Answer

Thus, the intensity of the reflected light is approximately \( 0.111 I_0 \).