Focal Length of Concave Mirror MCQs Quiz | Class 10

Understanding Focal Length of Concave Mirrors

A concave mirror is a converging mirror, meaning it converges parallel rays of light that fall on its surface after reflection. The focal length of a concave mirror is a fundamental property that dictates its behavior in forming images. Understanding how to determine this focal length, especially by using a distant object, is a key practical concept in optics for Class 10 Science.

Key Concepts

• Principal Axis: The straight line passing through the pole and the center of curvature of a spherical mirror.
• Pole (P): The center of the spherical mirror’s reflecting surface.
• Center of Curvature (C): The center of the sphere from which the mirror is cut.
• Radius of Curvature (R): The distance from the pole to the center of curvature (PC).
• Principal Focus (F): For a concave mirror, it is a point on the principal axis where rays of light parallel to the principal axis converge after reflection. It is a real focus.
• Focal Length (f): The distance from the pole to the principal focus (PF). For spherical mirrors with small apertures, the focal length is half of the radius of curvature (f = R/2).

Image Formation by a Distant Object

When an object is placed at a very large distance (effectively at infinity) from a concave mirror, the rays of light coming from it are considered to be parallel to each other and also parallel to the principal axis of the mirror. After reflection from the concave mirror, these parallel rays converge at a single point on the principal axis. This point is the principal focus (F) of the mirror.

The image formed under these conditions has the following characteristics:

• Position: At the principal focus (F).
• Nature: Real and inverted.
• Size: Highly diminished (often point-sized).

This phenomenon provides a simple and accurate method to determine the focal length of a concave mirror experimentally.

Measurement of Focal Length Using a Distant Object

This experiment is designed to find the approximate focal length of a concave mirror. Since the image of a distant object is formed at the principal focus, the distance from the mirror to this sharp image gives us the focal length.

Apparatus:

• Concave mirror
• Mirror holder/stand
• Small white screen (or a white wall/cardboard)
• Metre scale or measuring tape
• A distant object (e.g., a tree, a building, a window frame outside)

Procedure:

1. Mount the concave mirror on a suitable stand.
2. Face the concave mirror towards a well-illuminated distant object (e.g., a distant tree or building outside a window).
3. Place the white screen in front of the concave mirror, between the mirror and the distant object.
4. Move the screen forward or backward slowly until a sharp, clear, and inverted image of the distant object is formed on the screen.
5. Once a clear image is obtained, measure the distance between the pole of the concave mirror and the screen using the metre scale.
6. This measured distance is the approximate focal length (f) of the concave mirror.
7. Repeat the experiment a few times with different distant objects to ensure accuracy and take the average of the readings.

Note: It is crucial to use a distant object so that the incident rays can be considered parallel. This ensures the image forms precisely at the focal point.

Quick Revision Points

• Concave mirrors are converging mirrors.
• Focal length (f) is the distance from the pole to the principal focus.
• For a distant object, light rays are parallel to the principal axis.
• Parallel rays converge at the principal focus after reflection from a concave mirror.
• The image of a distant object is real, inverted, and highly diminished.
• The distance between the mirror and the sharp image of a distant object is its focal length.
• f = R/2 for small aperture mirrors.

Practice Questions

1. What type of image is formed by a concave mirror when the object is at infinity?
2. Why is it important to use a distant object when determining the focal length of a concave mirror experimentally?
3. If the radius of curvature of a concave mirror is 30 cm, what is its focal length?
4. List two characteristics of the image formed when parallel rays from a distant object fall on a concave mirror.
5. Describe briefly the steps to find the focal length of a concave mirror using the distant object method.