Class 10 · CBSE / NCERT · Physics

Light — Reflection and Refraction — Class 10

Mirrors and lenses are pure pattern once you nail the sign convention. Use the image solver to get v, magnification and the nature of the image for any case, then practise numericals.

Reflection of lightLight bounces off a surface so that the angle of incidence equals the angle of reflection. Spherical mirrors are concave (converging) or convex (diverging).

Refraction & refractive indexLight bends when it changes medium. Refractive index n = c/v = (speed in vacuum)/(speed in medium) = sin i / sin r (Snell's law).

Mirror & lens formulaMirror: 1/v + 1/u = 1/f. Lens: 1/v − 1/u = 1/f. Use the New Cartesian sign convention (distances against the incident light are negative).

Magnification & PowerMagnification m = h′/h. For mirrors m = −v/u, for lenses m = v/u. Power of a lens P = 1/f (f in metres), unit dioptre (D).

Lens & mirror image solver Interactive

Pick a mirror or lens, enter the object distance and focal length, and get the image distance, magnification and nature — sign convention applied for you.

Device Object distance (cm, in front) Focal length magnitude (cm)

Image distance, v—cm

Magnification, m—

Numericals practice Interactive

Refractive index, power and focal-length problems with full steps.

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Solved numericals

Q1. An object is placed 15 cm in front of a concave mirror of focal length 10 cm. Find the image distance and magnification.

Given: u = −15 cm, f = −10 cm

1/v = 1/f − 1/u = −1/10 + 1/15 = (−3+2)/30 = −1/30

v = −30 cm (real image, in front of the mirror)

m = −v/u = −(−30)/(−15) = −2 (inverted, twice the size)

Q2. A convex lens of focal length 20 cm forms an image of an object placed 30 cm away. Find v and the magnification.

Given: u = −30 cm, f = +20 cm

1/v = 1/f + 1/u = 1/20 − 1/30 = 1/60

v = +60 cm (real, on the other side)

m = v/u = 60/(−30) = −2 (inverted, magnified)

Formula sheet

Quantity	Formula	SI unit
Mirror formula	1/v + 1/u = 1/f	— (f = R/2)
Lens formula	1/v − 1/u = 1/f	—
Magnification (mirror)	m = −v/u = h′/h	—
Magnification (lens)	m = v/u = h′/h	—
Refractive index	n = c/v = sin i / sin r	— (no unit)
Power of a lens	P = 1/f (metres)	dioptre (D)

Common mistakes & exam wins

Real object ⇒ u is always negative in the New Cartesian sign convention.
Concave mirror & convex lens converge light (real images possible); convex mirror & concave lens always give a virtual, erect, diminished image.
Magnification: negative ⇒ real & inverted; positive ⇒ virtual & erect.
For a mirror f = R/2; light bends towards the normal when entering a denser medium.

Frequently asked questions

What is the difference between a concave and a convex mirror?

A concave mirror converges light and can form real or virtual images; a convex mirror diverges light and always forms a small, virtual, erect image (used as a rear-view mirror).

What is refractive index?

It is the ratio of the speed of light in vacuum to its speed in the medium, n = c/v, and also equals sin i / sin r (Snell's law).

What is the mirror formula?

1/v + 1/u = 1/f, where v is image distance, u is object distance and f is focal length (with f = R/2).

What is the power of a lens?

Power P = 1/f (f in metres), measured in dioptres (D). Convex lenses have positive power, concave lenses negative.