Ray Optics Fundamentals
Concave Mirror Image Formation
Investigate how concave mirrors converge light rays. Slide a glowing candle on an optical track to project real inverted images, move a card close to inspect makeup mirror close-up magnification, and focus parallel sunlight rays onto a solar cooker pot.
Concave Mirror Virtual Lab
Animate sliding candles, close-up vanity mirrors, and outdoor solar concentrators.
Live Telemetry
Formula: 1/f = 1/u + 1/v- Object Distance (u)
- -120.0 cm
- Image Distance (v)
- -60.0 cm
- Focal Length (f)
- -40.0 cm
- Radius (R)
- -80.0 cm
- Magnification (m)
- -0.50
Nature of Reflection in Concave Mirrors
A concave mirror is a curved mirror where the reflecting surface is curved inward. Because it causes parallel incoming light rays to gather or meet at a single focal point, it is also known as a converging mirror.
Principal Parameters
- Pole (P): The center of the reflecting surface of the mirror.
- Center of Curvature (C): The center of the sphere from which the mirror was cut.
- Principal Axis: The horizontal line passing through the Pole (P) and Center of Curvature (C).
- Principal Focus (F): The point on the principal axis where all rays parallel to the axis converge after reflection.
- Focal Length (f): The distance from the pole to the focus ($PF = f$). It is always negative for a concave mirror under Cartesian sign conventions:
Rules for Ray Construction
To find the position and nature of an image, we draw at least two of these principal rays from the object\'s tip:
- Rule 1 (Parallel Ray): A ray starting parallel to the principal axis reflects passing directly through the Focus (F).
- Rule 2 (Focal Ray): A ray passing through the Focus (F) reflects parallel to the principal axis.
- Rule 3 (Center Ray): A ray passing through the Center of Curvature (C) strikes the mirror surface perpendicularly (along the normal) and reflects back along the same path.
- Rule 4 (Pole Ray): A ray striking the Pole (P) reflects symmetrically, obeying the law of reflection (angle of incidence = angle of reflection).
Image Formation Cases
Unlike convex mirrors, a concave mirror forms images of varying sizes, orientations, and types depending on the object's position:
Object Beyond C
The image is formed **between C and F**. It is **real, inverted, and diminished** (smaller than the object).
Object At C
The image is formed **exactly at C**. It is **real, inverted, and of the exact same size** as the object ($m = -1$).
Object Between C and F
The image is formed **beyond C**. It is **real, inverted, and magnified** (enlarged).
Object Inside Focus (u < f)
The image is formed **behind the mirror**. It is **virtual, upright, and magnified**. This case explains shaving/makeup mirrors.
Practical Applications
- Shaving & Makeup Mirrors: Placing your face inside the focal length produces a magnified, upright virtual image for detail.
- Dentist Mirrors: Small concave mirrors help dentists see enlarged virtual reflections of teeth.
- Searchlights & Headlights: A light bulb placed at the focus (F) reflects parallel rays to form a powerful parallel beam.
- Solar Cookers: Concave reflectors concentrate parallel sunlight rays onto a focal point where a cooking pot is placed, generating extreme heat.
Solved Examples
Example 1
A candle of height 4.0 cm is placed 30.0 cm in front of a concave mirror of focal length 10.0 cm. Find the position, size, and properties of the image formed.
View Step-by-Step Solution
Final Answer:
Example 2
A dental patient sits 8.0 cm in front of a dentist's concave mirror of focal length 12.0 cm. Find the location of the tooth's image, the magnification, and state the properties of the image.
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Final Answer:
Example 3
An object is placed in front of a concave mirror of radius of curvature 40.0 cm. If the mirror produces a real inverted image that is 4 times larger than the object, find the object distance.
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Final Answer:
Self-Check Questions
Question 1
State the rules of reflection for principal rays incident on a concave mirror.
Show Answer & Explanation
There are four key ray construction rules for concave mirrors: (1) A ray parallel to the principal axis reflects through the principal focus (F). (2) A ray passing through the principal focus (F) reflects parallel to the principal axis. (3) A ray passing through the center of curvature (C) reflects back along the same path (since it hits the mirror normally). (4) A ray incident at the pole (P) reflects symmetrically at an equal angle relative to the principal axis (i = r).
Question 2
Draw a comparison of the image properties when an object is placed: (a) at the focus (F) and (b) inside the focus (u < f).
Show Answer & Explanation
(a) When the object is at F, the reflected rays emerge parallel. They never meet in front of the mirror and do not diverge behind it; they are traced to intersect at infinity. The image is real, inverted, and highly magnified. (b) When the object is inside F (between F and P), the reflected rays diverge. Traced backward behind the mirror, they intersect to form a virtual, upright, and magnified image. This is the only position where a concave mirror forms a virtual image.
Question 3
Why do searchlights and vehicle headlights use concave reflectors? Where is the light source placed?
Show Answer & Explanation
Searchlights and vehicle headlights use concave reflectors to produce a strong, parallel beam of light that travels long distances without scattering. The light source (bulb) is placed exactly at the mirror's principal focus (F). According to the rules of ray construction, any light rays originating from the focus will reflect parallel to the principal axis, creating a concentrated forward-pointing beam.
Question 4
Explain why a real image formed by a concave mirror is always inverted, while a virtual image is always upright.
Show Answer & Explanation
This is a consequence of coordinate ray crossing. For an object point above the principal axis, light rays passing through C or F cross the principal axis before converging at the real image point in front of the mirror. This crossing flips the y-coordinate, resulting in an inverted image. For virtual images, the reflected rays diverge in front of the mirror, meaning they never cross the axis in physical space. Their virtual back extensions intersect behind the mirror without crossing, keeping the y-coordinate above the axis and resulting in an upright image.