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1/f = 1/v + 1/u

PHY017 · Optics · Classes 10–12

Concave mirror

Objective: To study image formation by a concave mirror and find its focal length.

🧰 Apparatus

  • Concave mirror on a stand
  • Metre scale or optical bench
  • Candle
  • White screen

📐 Formulas and SI units

1/v + 1/u = 1/f (cm)
m = −v/u
R = 2f

💡 Theory

A concave mirror converges parallel rays to its focus F. Using the mirror formula 1/v + 1/u = 1/f with the NCERT sign convention (f negative), objects beyond F give real, inverted images in front of the mirror; objects inside F give virtual, upright, magnified images behind it.

🪜 Procedure

  1. Focus a distant object on a screen to estimate f.
  2. Place a candle beyond C and move the screen to find a sharp image.
  3. Record u and v (both negative for real images).
  4. Move the candle to C, between C and F, and inside F; note the image each time.
  5. Calculate f from each pair and take the mean.

📋 Observations Simulated values

✅ Result and conclusion

With f = −10 cm and u = −30 cm, the image is at v = −15 cm, real, inverted and half the size.

🔬 In a real lab

The mirror is not a perfect paraboloid, so wide beams blur (spherical aberration). Reading v to the sharpest point carries ±0.3 cm uncertainty.

⚠️ Safety

Never point a concave mirror at the Sun: it focuses heat strongly and can burn or blind.

❓ Quick check

1. An object at C of a concave mirror forms an image…

2. Which mirror is used as a shaving mirror?

3. For a concave mirror in the NCERT convention, f is…

🏋️ Practice

Easyf = −15 cm, u = −30 cm. v?

Answer: −30 cm

Mediumf = −10 cm, u = −5 cm. v and nature?

Answer: +10 cm, virtual, upright, ×2

ChallengeR = 40 cm. f?

Answer: 20 cm (−20 cm in sign convention)