A ray of light is incident upon a parallel sided transparent slab of thickness 9 cm at an angle of incidence 60° • If the angle of refraction is 30°, the lateral displacement of the light ray is

Options

A. `sqrt(3)cm`
B. `3sqrt(3)cm`
C. `3cm`
D. `2/sqrt(3)` cm

Explanation

To solve the problem of finding the lateral displacement of a light ray passing through a parallel-sided transparent slab, we can follow these steps:

### Step-by-Step Solution:

1. **Identify Given Values:**
- Thickness of the slab (t) = 9 cm
- Angle of incidence (i) = 60°
- Angle of refraction (r) = 30°

2. **Understand the Formula for Lateral Displacement:**
The formula to calculate the lateral displacement (x) of a light ray passing through a parallel-sided slab is given by:
\[ x = t \cdot \frac{\sin(i - r)}{\cos(r)} \]
where:
- \(i\) is the angle of incidence,
- \(r\) is the angle of refraction,
- \(t\) is the thickness of the slab.

3. **Calculate the Angle Difference:**
First, we need to calculate \(i - r\):
\[ i - r = 60° - 30° = 30° \]

4. **Substitute Values into the Formula:**
Now, we substitute the values into the formula:
\[ x = 9 \cdot \frac{\sin(30°)}{\cos(30°)} \]

5. **Calculate \(\sin(30°)\) and \(\cos(30°)\):**
- \(\sin(30°) = \frac{1}{2}\)
- \(\cos(30°) = \frac{\sqrt{3}}{2}\)

6. **Substitute the Trigonometric Values:**
Now substitute these values back into the equation:
\[ x = 9 \cdot \frac{\frac{1}{2}}{\frac{\sqrt{3}}{2}} = 9 \cdot \frac{1}{\sqrt{3}} \]

7. **Simplify the Expression:**
\[ x = \frac{9}{\sqrt{3}} = 3\sqrt{3} \text{ cm} \]

8. **Final Answer:**
The lateral displacement of the light ray is:
\[ x = 3\sqrt{3} \text{ cm} \]