Concave Mirror – Ray Diagrams, Formula & Real-Life Uses

A concave mirror (or converging mirror) is a spherical mirror with a reflecting surface curved inward. Unlike flat mirrors, concave mirrors focus light to a single point, making them essential in telescopes, headlights, and scientific instruments.

Key Properties:

• Converges parallel light rays

• Forms real or virtual images

• Has a positive focal length

• Used for magnification and focusing

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Basic Terminology

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Image Formation Rules & Ray Diagrams

Rule 1: Parallel Ray

A ray parallel to the principal axis reflects through the focus (F).

Rule 2: Focal Ray

A ray passing through F reflects parallel to the principal axis.

Rule 3: Central Ray

A ray passing through C reflects back along itself.

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Image Formation Cases

1. Object Beyond C

• Image Position: Between C and F

• Nature: Real, inverted, diminished

• Example: Astronomical telescopes

2. Object at C

• Image Position: At C

• Nature: Real, inverted, same size

• Example: Solar concentrators

3. Object Between C and F

• Image Position: Beyond C

• Nature: Real, inverted, magnified

• Example: Projector systems

4. Object at F

• Image Position: At infinity

• Nature: Highly magnified, real

• Example: Searchlights

5. Object Between F and P

• Image Position: Behind the mirror

• Nature: Virtual, erect, magnified

• Example: Makeup/shaving mirrors

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Mirror Formula & Magnification

1. Mirror Equation

1f=1u+1vf1​=u1​+v1​

• $f$ = Focal length

• $u$ = Object distance (negative)

• $v$ = Image distance (negative for real images)

2. Magnification Formula

m=−vu=hihom=−uv​=ho​hi​​

• If $|m|>1$ → Magnified image

• If $m$ is negative → Inverted image

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Sign Convention (Cartesian System)

• Object distance (u): Negative (left of mirror)

• Image distance (v): Negative for real images

• Focal length (f): Negative for concave mirrors

• Height above axis: Positive

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Real-Life Applications

1. Astronomical Telescopes

• Function: Collects light from distant stars

• Why Concave?: Large aperture gathers maximum light

2. Vehicle Headlights

• Function: Produces parallel beam

• Design: Bulb at focus → Parallel rays after reflection

3. Shaving/Makeup Mirrors

• Function: Magnifies facial features

• Design: Object between F and P → Virtual, erect image

4. Solar Furnaces

• Function: Concentrates sunlight

• Design: Large concave mirror focuses rays at focal point

5. Medical Uses

• Dentist Mirrors: Magnifies teeth

• ENT Instruments: Examines ear/nose/throat

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Concave vs. Convex Mirrors

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Solved Numerical Problems

Problem 1:

An object is placed 30 cm from a concave mirror (f = -15 cm). Find image position.
Solution:

1−15=1−30+1v  ⟹  v=−30 cm−151​=−301​+v1​⟹v=−30 cm

(Real image at 30 cm)

Problem 2:

A 4 cm object is placed 10 cm from a concave mirror (f = -20 cm). Find image height.
Solution:

1−20=1−10+1v  ⟹  v=−20 cm−201​=−101​+v1​⟹v=−20 cmm=−−20−10=−2  ⟹  hi=4×(−2)=−8 cmm=−−10−20​=−2⟹hi​=4×(−2)=−8 cm

(Inverted, magnified image)

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FAQs About Concave Mirrors

❓ Can concave mirrors form virtual images?

Yes, when the object is between F and P.

❓ Why is focal length negative?

By sign convention (light travels left to right).

❓ Are all converging mirrors concave?

Yes – concave mirrors are the only converging mirrors.

❓ How is a concave mirror made?

By silvering the outer surface of a glass sphere section.

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Conclusion

Concave mirrors are indispensable tools that:
✔ Focus light for scientific instruments
✔ Magnify objects for daily use
✔ Enable energy concentration in solar tech

Key Takeaways:

• Use ray diagrams to predict image properties

• Apply mirror formula 1f=1u+1vf1​=u1​+v1​

• Remember virtual images form when object is inside F

Experiment Idea: Use a spoon’s inner surface as a concave mirror to observe image changes!