A student determines the focal length of a device 'X' by focusing the image of a distant object on a screen placed 20 cm from the device on the same side as the object. The device 'X' is

Options

A. Concave lens of focal length 10 cm
B. Convex lens of focal length 20 cm
C. Concave mirror of focal length 10 cm
D. Concave mirror of focal length 20 cm

Explanation

To determine the focal length of the device 'X', we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Setup**: The student is focusing the image of a distant object on a screen placed 20 cm from the device. This indicates that the device is capable of forming an image at a specific distance.

2. **Understanding the Concept of Focal Length**: For optical devices, the focal length (f) is the distance from the device to the point where parallel rays of light converge (focus). When the object is at infinity, the image is formed at the focal point of the device.

3. **Analyzing the Given Distance**: The screen is placed 20 cm from the device. Since the object is at infinity, the image formed will be at the focal point of the device.

4. **Relating Focal Length to the Screen Distance**: In this case, since the image of a distant object (at infinity) is focused on the screen, the distance from the device to the screen (20 cm) is equal to the focal length of the device.

5. **Conclusion**: Therefore, the focal length of device 'X' is 20 cm.

6. **Identifying the Type of Device**: Since the image is formed on the same side as the object, this suggests that the device is a concave mirror, which reflects light rays back to the same side.

### Final Answer:
The device 'X' is a **concave mirror** with a focal length of **20 cm**.

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