Ray Optics Fundamentals
Magnification by Mirror
Explore how spherical mirrors change the size and orientation of reflections. Transition between a bathroom counter makeup mirror, a school optics bench with a vertical height scale, and a car side mirror showing diminished traffic.
Mirror Magnification virtual lab
Animate real-world setups to witness size, upright/inverted, and real/virtual changes in action.
Live Telemetry
Substitution: m = h_i / h_o = -v / u- Mirror Type
- Concave
- Object Height (hₒ)
- 40.0 cm
- Image Height (hᵢ)
- -80.0 cm
- Magnification (m)
- -2.00
- Object Dist (u)
- -60.0 cm
- Image Nature
- Real, Inverted
What is Mirror Magnification?
In spherical optics, **linear magnification** ($m$) describes the factor by which the size of an image changes relative to the size of the original object. It is mathematically defined as the ratio of the height of the image ($h_i$) to the height of the object ($h_o$):
This formula combines both height and distance ratios. The negative sign in the distance ratio ($-v/u$) ensures that orientation and Cartesian sign rules remain consistent:
Understanding the Sign of Magnification ($m$)
The sign of the magnification value directly tells us the **orientation** and **nature** of the image:
- Positive Magnification ($m > 0$): Indicates that the image is **upright (erect)**. Upright images formed by a single spherical mirror are always **virtual** (located behind the mirror plane).
- Negative Magnification ($m < 0$): Indicates that the image is **inverted (upside down)**. Inverted images formed by a single spherical mirror are always **real** (formed in front of the mirror, catchable on a physical screen).
Understanding the Magnitude of Magnification ($|m|$)
The absolute value of magnification determines the relative **size** of the image:
- $|m| > 1$: The image is **enlarged (magnified)**. (e.g., $m = +2.5$ represents a virtual upright image that is 2.5 times larger).
- $|m| < 1$: The image is **reduced (diminished)**. (e.g., $m = +0.4$ represents a virtual upright image that is 40% of the object's height).
- $|m| = 1$: The image is of the **same size** as the object. (e.g., $m = -1.0$ represents a real inverted image of identical height).
Concave vs. Convex Mirror Magnification Behavior
Concave Mirror (Converging)
Capable of producing **all types of magnification**:
- Inside focus ($u < f$): Magnification is positive and greater than 1 ($m > 1$). The image is virtual, upright, and enlarged (e.g., shaving/makeup mirror).
- Between C and F ($f < u < 2f$): Magnification is negative and greater than 1 ($m < -1$). The image is real, inverted, and enlarged.
- At C ($u = 2f$): Magnification is exactly $-1.0$. The image is real, inverted, and of the same size.
- Beyond C ($u > 2f$): Magnification is negative and between 0 and $-1$ ($-1 < m < 0$). The image is real, inverted, and diminished.
Convex Mirror (Diverging)
Produces only one specific magnification profile:
- For all physical object distances, the magnification $m$ is **always positive and less than 1** ($0 < m < 1$).
- The image is **always virtual, upright, and diminished**.
- This size reduction allows convex mirrors to pack a wide field of view into a small surface area, which is why they are utilized as automotive side mirrors and store security reflectors.
Solved Examples
Example 1
A shaving mirror of focal length 15.0 cm is placed 10.0 cm from a person's face. What is the magnification of the image, and is it upright or inverted?
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Final Answer:
Example 2
An object of height 5.0 cm is placed 30.0 cm in front of a convex mirror of focal length 20.0 cm. Determine the height of the image formed.
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Final Answer:
Example 3
A concave mirror forms a real image four times the size of the object. If the object is placed 15.0 cm in front of the mirror, find the focal length.
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Final Answer:
Self-Check Questions
Question 1
What does it mean physically when the magnification of a mirror is exactly -1?
Show Answer & Explanation
A magnification of m = -1 means that: (1) The negative sign indicates the image is real and inverted. (2) The magnitude of 1 indicates the image is exactly the same size as the object (h_i = h_o). This occurs for a concave mirror when the object is placed exactly at the Center of Curvature (u = -2f).
Question 2
Why is the magnification of a convex mirror always positive and less than 1?
Show Answer & Explanation
For a convex mirror, the focal length is positive (f > 0) and the object distance is negative (u < 0). According to the mirror formula, the image distance v = (f * u) / (u - f) is always positive, meaning it forms a virtual image behind the mirror. The magnification m = -v/u = -v / (-|u|) = v/u is always positive (upright) and since v < |u| is always true, the magnification magnitude is always less than 1, yielding a diminished image.
Question 3
Can a concave mirror produce a virtual, diminished image?
Show Answer & Explanation
No. A concave mirror can produce: (1) Real and diminished images (when object is beyond C, u > 2f). (2) Real and magnified images (when object is between C and F, f < u < 2f). (3) Virtual and magnified images (when object is inside F, u < f). It can never produce a virtual diminished image for a real object.
Question 4
How does linear magnification differ from angular magnification?
Show Answer & Explanation
Linear (or lateral) magnification is the ratio of the height of the image to the height of the object measured perpendicular to the principal axis. Angular magnification is the ratio of the angle subtended by the image at the eye to the angle subtended by the object, which is used for viewing instruments like microscopes or telescopes.