JEE Physics — Ray Optics Complete Chapter Guide

Chapter Overview & Weightage

Ray Optics is one of those chapters where the effort-to-marks ratio works heavily in your favour. Consistent 1–2 questions every year, predictable question patterns, and formulas that are directly applicable without much derivation — this is a scoring topic if you nail the conceptual clarity.

🎯 Exam Insider

Weightage trend (JEE Main): Ray Optics contributes roughly 5–7% of the Physics paper — typically 1–2 questions. JEE Advanced tests it more conceptually, often clubbing it with wave optics.

Year	JEE Main Q's	Marks	Topic Focus
2024	2	8	Lens combinations, TIR
2023	1	4	Mirror formula + magnification
2022	2	8	Prism deviation, lens maker's equation
2021	1	4	Equivalent mirror concept
2020	2	8	Optical instruments, TIR

The chapter has been tested continuously since JEE Main's inception. Questions alternate between formula-based (plug-and-solve) and concept-based (qualitative reasoning about image nature). Both are fully crackable.

Key Concepts You Must Know

Prioritised by how often they actually show up:

Tier 1 — Appears almost every year:

Mirror formula and sign convention (Cartesian — this trips up more students than any other topic)
Lens formula, magnification, and power of a lens
Snell's law and its applications at curved surfaces
Critical angle and total internal reflection conditions

Tier 2 — High frequency, slightly more involved:

Refraction at a single spherical surface
Lens maker's equation and its assumptions
Prism — minimum deviation, angle of deviation formula
Combination of lenses in contact and separated by a distance

Tier 3 — Asked occasionally, usually in JEE Advanced:

Silvered lens (equivalent mirror) — very popular in Advanced
Optical instruments: simple microscope, compound microscope, telescope
Displacement method for finding focal length

Important Formulas

Mirror Formula

$\frac{1}{v} + \frac{1}{u} = \frac{1}{f} = \frac{2}{R}$

When to use: Any problem involving a concave or convex mirror. Always apply Cartesian sign convention first — incident light travels left to right, distances measured from the pole.

Magnification: $m = -\frac{v}{u}$

Negative $m$ means inverted image.

Refraction at Spherical Surface

$\frac{n_2}{v} - \frac{n_1}{u} = \frac{n_2 - n_1}{R}$

When to use: Single refracting surface problems — glass sphere, glass slab with curved faces, fish-in-water type questions.

Lens Formula & Lens Maker's Equation

$\frac{1}{v} - \frac{1}{u} = \frac{1}{f}$

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

When to use: Lens formula for any thin lens problem. Lens maker's equation when the refractive index or radii of curvature are given — check $R$ sign convention carefully (centre of curvature direction).

Critical Angle & TIR

$\sin C = \frac{1}{n} = \frac{n_2}{n_1}$

When to use: Whenever a ray goes from denser to rarer medium. TIR occurs only when angle of incidence exceeds $C$ — not equals.

Prism Formulas

$A + r_1 + r_2 = 180° \quad \text{(wrong — see below)}$

Correct: $r_1 + r_2 = A$

$\delta = (i_1 + i_2) - A$

At minimum deviation: $i_1 = i_2 = i$ , $r_1 = r_2 = r = A/2$

$n = \frac{\sin\left(\frac{A + D_m}{2}\right)}{\sin\left(\frac{A}{2}\right)}$

Power & Combination of Lenses

$P = \frac{1}{f(\text{in metres})} \quad \text{(in dioptres)}$

Lenses in contact: $P = P_1 + P_2$ , equivalently $\frac{1}{f} = \frac{1}{f_1} + \frac{1}{f_2}$

Lenses separated by distance $d$ : $\frac{1}{f} = \frac{1}{f_1} + \frac{1}{f_2} - \frac{d}{f_1 f_2}$

Silvered Lens (Equivalent Mirror)

$P_{eq} = P_{\text{lens}} + P_{\text{mirror}} + P_{\text{lens}} = 2P_L + P_M$

$f_{eq} = \frac{1}{P_{eq}}$

When to use: When a lens has one silvered face, treat it as a mirror. This is a JEE Advanced favourite — it appeared in 2019 and 2022.

Solved Previous Year Questions

PYQ 1 — JEE Main 2024 Shift 1

A convex lens of focal length 20 cm is placed coaxially with a convex mirror of radius of curvature 20 cm. The separation between them is 15 cm. A point object is placed 60 cm in front of the lens. Find the position of the final image.

Solution:

Step 1 — Image through the lens first.

Using lens formula with $u = -60$ cm, $f = +20$ cm: $\frac{1}{v} - \frac{1}{-60} = \frac{1}{20}$ $\frac{1}{v} = \frac{1}{20} - \frac{1}{60} = \frac{3-1}{60} = \frac{2}{60}$ $v = +30 \text{ cm (behind the lens)}$

Step 2 — This image acts as the object for the convex mirror. The mirror is 15 cm behind the lens, so the object for the mirror is $30 - 15 = 15$ cm behind the mirror — i.e., $u = +15$ cm (virtual object, behind the mirror).

Mirror focal length: $f = R/2 = +10$ cm (convex mirror, positive).

$\frac{1}{v} + \frac{1}{u} = \frac{1}{f}$ $\frac{1}{v} + \frac{1}{15} = \frac{1}{10}$ $\frac{1}{v} = \frac{1}{10} - \frac{1}{15} = \frac{1}{30}$ $v = +30 \text{ cm}$

Positive $v$ from the mirror means the image is 30 cm behind the mirror — it's virtual, located 45 cm behind the lens.

⚠️ Common Mistake

Most students forget to convert the object distance for the mirror correctly. The image formed by the lens is behind the mirror (virtual object). Missing this sign kills the entire solution.

PYQ 2 — JEE Main 2023

A ray of light passes through an equilateral prism such that the angle of incidence equals the angle of emergence and each is equal to $\frac{3}{4}$ of the angle of the prism. Find the angle of deviation.

Given: $A = 60°$ , $i = e = \frac{3}{4} \times 60° = 45°$

Since $i = e$ , the prism is at minimum deviation.

$\delta = i + e - A = 45° + 45° - 60° = 30°$

That's it. When $i = e$ , minimum deviation condition is satisfied, and the formula is direct.

💡 Expert Tip

For equilateral prisms with $i = e$ , always check if it's a minimum deviation situation. It usually is — and that halves your calculation time.

PYQ 3 — JEE Advanced 2022 (Concept-based)

A biconvex lens (both radii = 30 cm, $n = 1.5$ ) has its right face silvered. An object is placed 30 cm in front. Find the position of the final image.

Using the silvered lens formula:

First, find $f$ of the lens: $\frac{1}{f_L} = (1.5-1)\left(\frac{1}{30} - \frac{1}{-30}\right) = 0.5 \times \frac{2}{30} = \frac{1}{30}$ So $f_L = 30$ cm, $P_L = \frac{1}{0.30}$ D (but we work in cm here).

Mirror: silvered convex surface with $R = 30$ cm, so $f_M = 15$ cm, $P_M = \frac{1}{15}$ (in cm $^{-1}$ ).

Equivalent power: $P_{eq} = 2P_L + P_M = \frac{2}{30} + \frac{1}{15} = \frac{2}{30} + \frac{2}{30} = \frac{4}{30}$

$f_{eq} = \frac{30}{4} = 7.5 \text{ cm}$

Using mirror formula: $u = -30$ cm, $f = -7.5$ cm (acts as concave mirror): $\frac{1}{v} = \frac{1}{f} - \frac{1}{u} = \frac{1}{-7.5} - \frac{1}{-30} = -\frac{4}{30} + \frac{1}{30} = -\frac{3}{30}$ $v = -10 \text{ cm}$

Image is 10 cm in front of the lens — real, inverted.

Difficulty Distribution

For JEE Main Ray Optics questions:

Difficulty	% of Questions	What to Expect
Easy	40%	Direct formula application — mirror/lens formula, critical angle
Medium	45%	2-step problems — lens + mirror combination, prism with $i = e$
Hard	15%	Silvered lens, lens at non-contact separation, ray tracing in unusual media

🎯 Exam Insider

JEE Main has been consistently asking 1 medium-difficulty lens/mirror combination problem. These are fully solvable if your sign convention is rock-solid. JEE Advanced goes harder — expect silvered lenses, optical path length calculations.

Expert Strategy

Week 1 — Master sign convention. This is non-negotiable. Before touching a single formula, draw the principal axis, mark the pole, and consciously assign signs. Most wrong answers in this chapter come from sign errors, not formula ignorance.

Week 2 — Solve PYQs by type. Group past questions: all mirror problems together, all lens problems together, all prism problems together. You'll notice the same 4–5 structures repeating. Once you recognise the template, execution becomes mechanical.

💡 Expert Tip

For combination problems (lens + mirror), always find the intermediate image first, then use it as the object for the next optical element. Never try to do it in one step — you will make errors. Toppers do it step-by-step every single time.

For JEE Advanced specifically: Spend extra time on silvered lenses and refraction at spherical surfaces. The Advanced paper often asks you to derive an image position through multiple refractions, which requires the $\frac{n_2}{v} - \frac{n_1}{u} = \frac{n_2-n_1}{R}$ formula applied repeatedly.

Optical Instruments: Don't skip these for JEE Main. Formulae for magnifying power of microscope and telescope appear roughly once every 2–3 years. They're direct substitutions — 4 marks for 2 minutes of work.

Common Traps

⚠️ Common Mistake

Trap 1 — Wrong sign for $R$ in lens maker's equation. The convention: $R$ is positive if the centre of curvature is on the transmission side (right side for light going left to right). For a biconvex lens, $R_1 > 0$ and $R_2 < 0$ . Many students flip $R_2$ and get $\frac{1}{f}$ as negative — suddenly their convex lens is diverging.

⚠️ Common Mistake

Trap 2 — Virtual object sign. When a converging beam is intercepted by a lens or mirror before it converges, the convergence point is a virtual object. It lies on the same side as the outgoing light. Always draw the ray diagram first when the problem has multiple optical elements.

⚠️ Common Mistake

Trap 3 — Critical angle direction. TIR happens only when light goes from denser to rarer medium, and the angle of incidence exceeds the critical angle. Neither condition alone is sufficient. Examiners specifically test this with light hitting a glass-air interface at exactly the critical angle (refracted ray goes along the surface — no TIR yet).

⚠️ Common Mistake

Trap 4 — Power in dioptres vs. cm. The formula $P = 1/f$ requires $f$ in metres. When a problem gives focal lengths in cm, convert first. Combining powers in cm directly gives you a numerically wrong answer that still looks plausible.

⚠️ Common Mistake

Trap 5 — Magnification sign. $m = -v/u$ for mirrors. A positive magnification means erect image, negative means inverted. Students often confuse the sign of $m$ with whether the image is real or virtual — those are separate things. A real image from a concave mirror is inverted ( $m < 0$ ), but a virtual image (object inside focal length) is erect ( $m > 0$ ).

One last thing on prisms: The formula $n = \frac{\sin\frac{A+D_m}{2}}{\sin\frac{A}{2}}$ is only valid at minimum deviation. If the problem doesn't state minimum deviation, use Snell's law at each surface separately. Using the minimum deviation formula for a general case is one of the most common errors in JEE Main.