Class 12 Physics · NCERT notes for NEET

Ray Optics and Optical Instruments: NCERT Notes, Formulas and Tricks for NEET

The ray model of light: mirrors, refraction and TIR, lenses, prisms, and microscopes and telescopes. It is one of the most-asked Class 12 chapters in NEET, mostly through sign-convention numericals, so practise signs until they are automatic.

1. Reflection and spherical mirrors
2. Refraction and total internal reflection 🔒
3. Lenses and lens maker's formula 🔒
4. Prism and dispersion 🔒
5. Optical instruments 🔒

Topic 1 is open for everyone. The full chapter, quick revision and practice open with a plan, or start free with 5 full chapters.

Open the interactive version (simulations and tap-to-answer quick checks).

Topic 1

Reflection and spherical mirrors

The mirror on a car's side says "objects in mirror are closer than they appear". It is convex: it shrinks everything so you can see more road.

Laws of reflection: angle of incidence = angle of reflection, and the incident ray, reflected ray and normal lie in one plane. They hold for curved mirrors too, using the normal at the point of incidence.
Cartesian sign convention: measure every distance from the pole P. Along the incident light is $+$ , against it is $-$ . Heights above the axis are $+$ , below are $-$ .
So for a real object, $u < 0$ . A concave mirror has $f, R < 0$ ; a convex mirror has $f, R > 0$ .
For paraxial rays, $f = R /2$ . The focus F lies midway between P and the centre of curvature C.
Mirror equation $\frac{1}{v} + \frac{1}{u} = \frac{1}{f}$ works for both mirrors once you put the signs in.
Magnification $m = h^{'} / h = - v / u$ . $m < 0$ : real and inverted. $m > 0$ : virtual and erect. $∣ m ∣ > 1$ : magnified.
Concave mirror: object beyond C gives a real image between C and F; object at C gives image at C (same size); object at F gives image at infinity; object between F and P gives a virtual, erect, magnified image (shaving mirror).
Convex mirror: for any real object the image is virtual, erect, diminished and lies between P and F.
Focal length of a mirror does not depend on the surrounding medium or on the colour of light, so mirrors have no chromatic aberration.

Two easy rays fix the image: parallel ray reflects through F, ray through F reflects parallel. The orange image is real and inverted, between C and F.

For a convex mirror the reflected rays spread out; their dashed extensions meet behind the mirror, so the image is virtual, erect and small.

Every sign comes from this one picture: along incident light is +, against it is -; up is +, down is -. — Every sign comes from this one picture: along incident light is $+$ , against it is $-$ ; up is $+$ , down is $-$ .

Formulas

$f = \frac{R}{2}$
Paraxial rays; same sign as R
$\frac{1}{v} + \frac{1}{u} = \frac{1}{f}$
Mirror equation, with signs
$m = \frac{h ^{'}}{h} = - \frac{v}{u}$
Linear magnification of a mirror
$v = \frac{u f}{u - f}$
Mirror equation solved for v
$m = \frac{f}{f - u}$
Magnification without finding v first

Tips, tricks and hacks

Direct v formula

v = u f / (u - f)

. Concave

f = - 15

cm,

u = - 20

cm:

v = 300/ (- 5) = - 60

cm. One line, no fractions to add.

m straight from f and u

m = f / (f - u)

. Same example:

- 15/ (- 15 + 20) = - 3

. Real, inverted, 3 times bigger.

Convex mirror filterA real object in front of a convex mirror always gives

0 < m < 1

and

v > 0

. Strike out any option with a real, inverted or enlarged image.

Rotating plane mirrorTurn a plane mirror by

θ

and the reflected ray turns by

2 θ

. A

1 0^{\circ}

turn moves the spot by

2 0^{\circ}

Common mistakes

✗ Putting $f = + 15$ cm for a concave mirror because "focal length is a length".

✓ With the Cartesian convention the focus of a concave mirror is in front (against the light), so $f = - 15$ cm.

✗ Using the lens formula $1/ v - 1/ u = 1/ f$ for mirrors.

✓ Mirrors use $1/ v + 1/ u = 1/ f$ and $m = - v / u$ ; the minus-sign forms belong to lenses.

✗ Thinking a concave mirror always forms a real image.

✓ Object between F and P gives a virtual, erect, magnified image; that is how a shaving mirror works.

NEET traps

"Focal length of a mirror changes when it is dipped in water": FALSE. Only lenses change, because reflection does not involve n.

A question gives $m = + 2$ for a concave mirror and asks where the object is: positive m means virtual, so the object is between F and P, not beyond C.

Half the mirror painted black still forms the whole image, only dimmer.

Quick check: An object is 20 cm in front of a concave mirror of focal length 15 cm. The image is

60 cm in front, real, inverted, 3 times larger
60 cm behind, virtual, erect, 3 times larger
8.6 cm in front, real, inverted, smaller
12 cm behind, virtual, erect, smaller

Answer: A. $v = u f / (u - f) = (- 20) (- 15) / (- 5) = - 60$ cm (in front, real). $m = - v / u = - 3$ : inverted and 3 times larger.

Topic 2 · 🔒

Refraction and total internal reflection

Key points, graphs, every formula, tricks, common mistakes and NEET traps for this topic are inside Dhruv.

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Topic 3 · 🔒

Lenses and lens maker's formula

Key points, graphs, every formula, tricks, common mistakes and NEET traps for this topic are inside Dhruv.

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Topic 4 · 🔒

Prism and dispersion

Key points, graphs, every formula, tricks, common mistakes and NEET traps for this topic are inside Dhruv.

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Topic 5 · 🔒

Optical instruments

Key points, graphs, every formula, tricks, common mistakes and NEET traps for this topic are inside Dhruv.

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Practise Ray Optics and Optical Instruments questions

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