A light ray travelling parallel to the principal axis of a convex lens of focal length 12 cm strikes the lens at a height of 5 mm from the principal axis. What is the angle of deviation produced?

Options

A. `4^(@)`
B. `5^(@)`
C. `1^(@)`
D. `2.4^(@)`

Answer

To solve the problem of finding the angle of deviation produced by a light ray striking a convex lens, we can follow these steps:

### Step 1: Understand the Given Information
We have a convex lens with a focal length (f) of 12 cm. A light ray is traveling parallel to the principal axis and strikes the lens at a height of 5 mm from the principal axis.

### Step 2: Convert Units
Since the focal length is given in centimeters, we should convert the height from millimeters to centimeters for consistency:
- Height (h) = 5 mm = 0.5 cm

### Step 3: Identify the Properties of the Ray
The light ray is parallel to the principal axis, which means it is a paraxial ray. Such rays converge at the focal point after passing through the lens.

### Step 4: Draw a Diagram
Draw a diagram of the convex lens with the principal axis, focal point (F), and the incident ray striking the lens at a height of 0.5 cm. Mark the optical center (O) of the lens.

### Step 5: Determine the Triangle Formed
When the ray passes through the lens, it will converge towards the focal point. The height at which the ray strikes the lens (0.5 cm) and the distance from the optical center to the focal point (12 cm) will form a right triangle.

### Step 6: Calculate the Angle of Deviation
The angle of deviation (θ) can be found using the tangent function:
- \[ \tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} = \frac{h}{f} \]
Substituting the values:
- \[ \tan(\theta) = \frac{0.5 \text{ cm}}{12 \text{ cm}} = \frac{0.5}{12} \]

### Step 7: Calculate θ
Now, we can find θ:
- \[ \theta = \tan^{-1}\left(\frac{0.5}{12}\right) \]
Calculating this gives:
- \[ \theta \approx \tan^{-1}(0.04167) \approx 2.38^\circ \]

### Step 8: Round the Answer
Rounding to one decimal place, we get:
- \[ \theta \approx 2.4^\circ \]

### Final Answer
The angle of deviation produced is approximately **2.4 degrees**.

---