Mirror Formula MCQs Quiz | Class 10

Understanding Mirror Formula and its Applications

The mirror formula is a fundamental relationship in optics that describes the connection between the object distance (u), image distance (v), and focal length (f) of a spherical mirror. This formula is crucial for understanding how mirrors form images and for solving related numerical problems.

The Mirror Formula:

The mirror formula is given by:

1/f = 1/v + 1/u

Where:

• f is the focal length of the mirror.
• v is the image distance (distance of the image from the pole of the mirror).
• u is the object distance (distance of the object from the pole of the mirror).

Magnification Formula:

Magnification (m) describes how much larger or smaller an image is compared to the object, and whether it is inverted or erect.

m = hi / ho = -v / u

Where:

• hi is the height of the image.
• ho is the height of the object.

Key Sign Conventions for Spherical Mirrors:

To correctly apply the mirror formula, a consistent set of sign conventions is necessary:

1. Pole as Origin: All distances are measured from the pole of the mirror.
2. Incident Light Direction: Distances measured in the direction of incident light are taken as positive. Distances measured against the direction of incident light are taken as negative. (For practical purposes, this means distances to the left of the mirror are usually negative).
3. Principal Axis: Heights measured upwards from and perpendicular to the principal axis are taken as positive. Heights measured downwards are taken as negative.

Summary of Signs for Concave and Convex Mirrors:

Applications of Mirror Formula:

1. Locating Images: Given the object’s position and the mirror’s focal length, you can find the image’s position (v).
2. Determining Mirror Type: Based on image characteristics (real/virtual, erect/inverted, magnified/diminished) and given distances, you can deduce the type of mirror.
3. Calculating Focal Length: If object and image distances are known, the focal length can be calculated. This is used in experimental setups.
4. Understanding Image Characteristics: The sign of magnification tells you if the image is erect (+) or inverted (-). Its magnitude tells you if it’s magnified (|m| > 1), diminished (|m| < 1), or same size (|m| = 1).

Quick Revision Checklist:

• Mirror Formula: 1/f = 1/v + 1/u
• Magnification: m = hi / ho = -v / u
• Concave mirror f is negative. Convex mirror f is positive.
• Real images are formed in front of the mirror, v is negative, m is negative (inverted).
• Virtual images are formed behind the mirror, v is positive, m is positive (erect).
• Convex mirrors always form virtual, erect, and diminished images.
• Concave mirrors can form both real and virtual images depending on object position.

Practice Questions:

1. An object 4 cm high is placed at a distance of 15 cm from a concave mirror of focal length 10 cm. Find the position, nature, and size of the image.
2. A convex mirror used for rearview on an automobile has a radius of curvature of 3.00 m. If a bus is located at 5.00 m from this mirror, find the position, nature, and size of the image.
3. An object is placed at a distance of 12 cm from a concave mirror. The image formed is real, inverted, and 4 times magnified. Find the focal length of the mirror.
4. Where should an object be placed in front of a concave mirror of focal length 20 cm to obtain a real image two times magnified?
5. A magnifying mirror produces an erect image 3 times the size of an object placed 20 cm from it. What is the focal length of the mirror?