A ray of light is incident on a glass plate. The light ray travels distance of 5 cm inside the glass plate before emerging out of the glass plate. If the incident ray suffers a deviation of 30°, the perpendicular distance between incident and the emergent ray is

Options

A. 5cm
B. 2.5cm
C. 7.5cm
D. 10cm

Explanation

To solve the problem, we need to determine the perpendicular distance between the incident ray and the emergent ray after the light travels through the glass plate. This distance is known as the lateral shift.

### Step-by-Step Solution:

1. **Identify Given Information:**
- Distance traveled inside the glass plate (QR) = 5 cm
- Angle of deviation (i - r) = 30°

2. **Understand the Concept of Lateral Shift:**
- The lateral shift (x) can be calculated using the formula:
\[ x = QR \cdot \sin(i - r) \]
- Here, \(QR\) is the distance traveled in the medium (glass plate), and \((i - r)\) is the angle of deviation.

3. **Calculate the Sine of the Angle:**
- We need to find \(\sin(30°)\):
\[ \sin(30°) = \frac{1}{2} \]

4. **Substitute Values into the Formula:**
- Plug the values into the lateral shift formula:
\[ x = 5 \, \text{cm} \cdot \sin(30°) \]
\[ x = 5 \, \text{cm} \cdot \frac{1}{2} \]

5. **Perform the Calculation:**
- Calculate the lateral shift:
\[ x = 5 \, \text{cm} \cdot \frac{1}{2} = 2.5 \, \text{cm} \]

6. **Conclusion:**
- The perpendicular distance between the incident ray and the emergent ray is 2.5 cm.

### Final Answer:
The correct answer is 2.5 cm.