A beam of light travelling in water is incident on a glass which is immersed in the water. The incident beam…

1. Analyze the Question

We are given:

• Medium 1 (Incident medium): Water ($n_1 = 1.33$)
• Medium 2 (Refractive medium): Glass ($n_2 = 1.5$)
• Angle of incidence ($i$): $40^\circ$
• We need to find the angle of refraction ($r$).

2. Explain the Concept

To solve this, we use Snell’s Law of Refraction, which states:

Where:

• $n_1$ is the refractive index of the first medium.
• $i$ is the angle of incidence.
• $n_2$ is the refractive index of the second medium.
• $r$ is the angle of refraction.

3. Show the Solution

Step 1: Rearrange the formula to solve for $\sin(r)$:

Step 2: Plug in the given values:

Step 3: Calculate $\sin(40^\circ)$: Using a calculator, $\sin(40^\circ) \approx 0.6428$

Step 4: Perform the multiplication and division:

Step 5: Find the angle $r$ by taking the inverse sine ($\sin^{-1}$):

4. Identify the Answer

Comparing our result to the options provided, the calculated angle matches option D.

5. Exam Tip

When dealing with refraction between two media that are not air, always remember to use the refractive index of the first medium ($n_1$) instead of assuming it is 1. A common mistake students make is using $1 \times \sin(i) = n_2 \sin(r)$, which is only true if the light is traveling from air or a vacuum. Always check the "incident medium" carefully!