Magnification (Mirrors) MCQs Quiz | Class 10
This quiz is designed for Class X students, covering Subject Science (Code 086), Unit III: Natural Phenomena, focusing on the Topic: Magnification (Mirrors). It includes questions on the meaning of magnification, sign conventions, and basic numerical problems. Attempt all 10 multiple-choice questions, then click ‘Submit Quiz’ to see your score and ‘Download Answer PDF’ for a detailed answer sheet.
Understanding Magnification in Mirrors
Magnification is a crucial concept in understanding how images are formed by spherical mirrors. It tells us about the size and orientation of the image relative to the object. This section will help you grasp the meaning, sign conventions, and basic numerical applications of magnification.
What is Magnification?
Magnification (denoted by ‘m’) is defined as the ratio of the height of the image (h’) to the height of the object (h). It quantifies how much larger or smaller an image is compared to the object, and also indicates whether the image is erect or inverted.
The formula for linear magnification is:
m = h' / h
Additionally, for spherical mirrors, magnification can also be expressed in terms of object distance (u) and image distance (v):
m = -v / u
Where:
h'= height of the imageh= height of the objectv= image distance from the mirroru= object distance from the mirror
Sign Conventions for Magnification and Mirror Formula
To correctly apply the magnification formula and the mirror formula, a consistent set of sign conventions is essential. We follow the New Cartesian Sign Convention:
- All distances are measured from the pole (origin) of the mirror.
- Distances measured in the direction of incident light are taken as positive.
- Distances measured opposite to the direction of incident light are taken as negative.
- Heights measured upwards (above the principal axis) are taken as positive.
- Heights measured downwards (below the principal axis) are taken as negative.
Interpreting the Sign and Magnitude of Magnification (m):
| Aspect | Condition | Interpretation |
|---|---|---|
| Sign of m | m > 0 (Positive) | Image is Virtual and Erect |
| m < 0 (Negative) | Image is Real and Inverted | |
| Magnitude of m | |m| > 1 | Image is Magnified (larger than object) |
| |m| = 1 | Image is of the Same Size as object | |
| |m| < 1 | Image is Diminished (smaller than object) |
Basic Numerical Applications
Let’s look at how to apply these concepts in problems:
Example 1: Calculating Magnification from Heights
An object 5 cm tall is placed in front of a mirror. Its image is formed 10 cm tall and inverted. Calculate the magnification.
Solution:
Object height (h) = +5 cm
Image height (h’) = -10 cm (since it’s inverted)
Magnification (m) = h’ / h = -10 cm / +5 cm = -2
The negative sign indicates a real and inverted image, and the magnitude 2 indicates it’s magnified (twice the size of the object).
Example 2: Calculating Magnification from Distances
A concave mirror forms a real image at a distance of 30 cm from the mirror when an object is placed at 15 cm. Find the magnification.
Solution:
Object distance (u) = -15 cm (always negative for real objects)
Image distance (v) = -30 cm (negative for real image formed by concave mirror)
Magnification (m) = -v / u = -(-30 cm) / (-15 cm) = 30 / (-15) = -2
Again, the negative sign indicates a real and inverted image, and the magnitude 2 shows it’s magnified.
Quick Revision List
- Magnification (m) = h’ / h = -v / u.
- Positive ‘m’ means virtual and erect image.
- Negative ‘m’ means real and inverted image.
- |m| > 1 means magnified image.
- |m| = 1 means same size image.
- |m| < 1 means diminished image.
- Concave mirrors can produce real, virtual, magnified, diminished, or same-size images depending on object position.
- Convex mirrors always produce virtual, erect, and diminished images.
Practice Questions
- An object 4 cm high is placed in front of a concave mirror. If the real image formed is 8 cm high, what is the magnification?
- A convex mirror produces an image that is 0.5 times the size of the object. If the object is placed at 20 cm from the mirror, what is the image distance?
- For an image formed by a mirror, if m = +1.5, describe the nature and size of the image.
- If the object distance (u) is -10 cm and the image distance (v) is +5 cm, calculate the magnification.
- A mirror produces an image with magnification -0.5. What can you conclude about the image?
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