Class 12 — Ray Optics and Optical Instruments

Chapter Overview & Weightage

Ray Optics is one of the highest-weightage chapters in Class 12 Physics. Together with Wave Optics, it forms the Optics unit which carries 14 marks in the board paper. Pure Ray Optics typically gives 8–10 marks split across MCQs, short answers, and one long answer.

CBSE Class 12 Weightage (Year-by-Year)

Year	Marks	Question Type
2024	9	2 MCQ + SA + LA-5
2023	8	1 MCQ + 2 SA + 1 derivation
2022	10	LA on optical instruments + numerical
2021	8	Combination of mirror and lens

The 5-mark LA is often either lens-mirror combinations, or derivation of lensmaker’s formula / refraction at spherical surfaces.

Key Concepts You Must Know

Reflection and mirror formula — $\dfrac{1}{v} + \dfrac{1}{u} = \dfrac{1}{f}$ . Sign convention is everything.

Refraction and Snell’s law — $n_1 \sin\theta_1 = n_2 \sin\theta_2$ . Total internal reflection at the critical angle.

Lens formula — $\dfrac{1}{v} - \dfrac{1}{u} = \dfrac{1}{f}$ . Note: minus sign for lens, plus for mirror.

Lensmaker’s equation — $\dfrac{1}{f} = (n - 1)\left(\dfrac{1}{R_1} - \dfrac{1}{R_2}\right)$ .

Power of a lens — $P = 1/f$ (in metres). Combination: $P_{\text{total}} = P_1 + P_2 + \cdots$ .

Optical instruments — Microscope (compound and simple), telescope (astronomical and Galilean). Magnification formulas for normal adjustment and least distance of distinct vision.

Important Formulas

$\frac{1}{v} + \frac{1}{u} = \frac{1}{f}, \quad m = -\frac{v}{u} = \frac{h'}{h}$

Sign convention: distances measured against incident light direction are positive; concave mirror has $f < 0$ .

$\frac{1}{v} - \frac{1}{u} = \frac{1}{f}, \quad m = \frac{v}{u} = \frac{h'}{h}$

Convex lens: $f > 0$ ; concave: $f < 0$ . Object distance $u$ is conventionally negative.

$\frac{1}{f} = (n - 1)\left(\frac{1}{R_1} - \frac{1}{R_2}\right)$

For biconvex lens ( $R_1 > 0$ , $R_2 < 0$ ), simplifies to $\dfrac{1}{f} = (n-1) \cdot \dfrac{2}{R}$ for symmetric lens.

$\sin\theta_c = \frac{1}{n}$

For glass ( $n = 1.5$ ): $\theta_c \approx 41.8°$ . For water ( $n = 1.33$ ): $\theta_c \approx 48.6°$ .

Solved Previous Year Questions

PYQ 1 — CBSE 2024, 5 Marks

An object is placed 30 cm in front of a convex lens of focal length 20 cm. Find image position, magnification, and nature.

Given: $u = -30$ cm, $f = +20$ cm.

$\dfrac{1}{v} = \dfrac{1}{f} + \dfrac{1}{u} = \dfrac{1}{20} - \dfrac{1}{30} = \dfrac{3 - 2}{60} = \dfrac{1}{60}$ .

$v = 60$ cm. Magnification $m = v/u = -2$ . Image is real, inverted, and magnified (2× size).

PYQ 2 — CBSE 2023, 3 Marks

Derive the lens formula using refraction at two spherical surfaces.

Use the formula for refraction at a single spherical surface twice: first surface (light enters) and second surface (light exits). Add the two equations and the intermediate image cancels, giving $\dfrac{1}{v} - \dfrac{1}{u} = (n - 1)\left(\dfrac{1}{R_1} - \dfrac{1}{R_2}\right)$ .

PYQ 3 — CBSE 2022, 5 Marks

A compound microscope has objective focal length 1 cm and eyepiece focal length 5 cm, with tube length 25 cm. Find total magnification when image forms at near point (D = 25 cm).

$M_{\text{microscope}} = M_o \times M_e = \dfrac{L}{f_o}\left(1 + \dfrac{D}{f_e}\right) = \dfrac{25}{1}\left(1 + \dfrac{25}{5}\right) = 25 \times 6 = 150$ .

Difficulty Distribution

Difficulty	% of Marks	Sub-topics
Easy	30%	Mirror/lens single substitution, Snell’s law
Medium	50%	Lens-mirror combinations, magnification, lensmaker’s
Hard	20%	Optical instruments (microscope, telescope), TIR + prism

Expert Strategy

Week 1 — Sign convention and single-element problems. This is where most marks are won or lost. Practice 30+ problems of single mirror/lens until sign convention is automatic.

Week 2 — Combinations. Two-lens, lens + mirror, and immersed lens problems. Use $1/f_{\text{total}} = 1/f_1 + 1/f_2$ for thin lenses in contact.

Week 3 — Optical instruments. Memorise the four formulas (compound microscope and telescope, both at near point and infinity). They directly appear as 5-mark questions.

Sign convention masterstroke: Adopt the rule “object distance is always negative (real object)” and “image distance positive if real, negative if virtual” for both mirrors and lenses. One rule for both — no more confusion.

Common Traps

Trap 1: Confusing mirror formula sign convention with lens.

Mirror: $\dfrac{1}{v} + \dfrac{1}{u} = \dfrac{1}{f}$ (plus sign). Lens: $\dfrac{1}{v} - \dfrac{1}{u} = \dfrac{1}{f}$ (minus sign). They look similar — write them out fully every time.

Trap 2: Forgetting that $R_1$ and $R_2$ have signs in lensmaker’s equation.

For a biconvex lens, $R_1 > 0$ and $R_2 < 0$ . Plugging both as positive gives the wrong focal length.

Trap 3: Using normal adjustment formula when image is at near point.

Microscope $M = (L/f_o)(D/f_e)$ for image at infinity (normal adjustment); but $(L/f_o)(1 + D/f_e)$ for image at near point. Read the question carefully.

Trap 4: Ignoring the medium when computing critical angle.

$\sin\theta_c = n_2/n_1$ for light going from denser to rarer ( $n_1 > n_2$ ). The “1/n” form assumes the rarer medium is air ( $n_2 = 1$ ).

Trap 5: Wrong magnification sign.

For mirrors: $m = -v/u$ . For lenses: $m = v/u$ . The sign tells you upright (positive) vs inverted (negative). Don’t lose 1 mark on a sign.