⚡ Formula Bank

Reflection and Refraction

Snell's Law: n₁ sin(θ₁) = n₂ sin(θ₂) — n₁, n₂ are refractive indices, θ₁, θ₂ are angles of incidence and refraction
Refractive Index: n = c/v — c is speed of light in vacuum, v is speed of light in medium
Total Internal Reflection: sin(θ_c) = n₂/n₁ — θ_c is critical angle, n₁, n₂ are refractive indices
Mirror Formula: 1/f = 1/do + 1/di — f is focal length, do, di are object and image distances
Magnification: m = -di/do — m is magnification, di, do are image and object distances
Examiner's Trap: Students often confuse Snell's Law with the mirror formula.

Spherical Mirrors

Mirror Equation: 1/f = 1/do + 1/di — f is focal length, do, di are object and image distances
Focal Length: f = R/2 — R is radius of curvature
Radius of Curvature: R = 2f — R is radius of curvature, f is focal length
Magnification: m = -di/do = hi/h_o — m is magnification, hi, h_o are image and object heights
Examiner's Trap: Students often mix up the signs of object and image distances.

Refraction through Lenses

Lensmaker's Formula: 1/f = (n-1)(1/R₁ - 1/R₂) — f is focal length, n is refractive index, R₁, R₂ are radii of curvature
Lens Equation: 1/f = 1/do + 1/di — f is focal length, do, di are object and image distances
Magnification: m = -di/do = hi/h_o — m is magnification, hi, h_o are image and object heights
Power of Lens: P = 1/f — P is power, f is focal length in meters
Examiner's Trap: Students often struggle with the signs of radii of curvature.

Optical Instruments

Telescope Magnification: m = -f_o/f_e — m is magnification, f_o, f_e are objective and eyepiece focal lengths
Microscope Magnification: m = (L/f_o)(D/f_e) — m is magnification, L is tube length, f_o, f_e are objective and eyepiece focal lengths, D is least distance of distinct vision
Examiner's Trap: Students often get confused between the magnifications of telescopes and microscopes.

Which Formula When?

Situation	Relevant Formulas
Refraction through a surface	Snell's Law, Refractive Index
Spherical mirrors	Mirror Equation, Focal Length, Radius of Curvature
Lenses	Lensmaker's Formula, Lens Equation, Power of Lens
Optical Instruments	Telescope Magnification, Microscope Magnification

🪤 The 5 Mistakes That Cost Marks

The 5 Mistakes That Cost Marks

Mistake 1 — Mirror Madness:
🔴 What students write: Using 1/f = 1/do + 1/di for a plane mirror, where f → ∞.
✅ What examiners expect: For a plane mirror, image distance equals object distance (di = -do), and magnification m = -1.
💸 Marks lost: 2 marks
🔧 The fix (30-second trick): Recall that for a plane mirror, the image is virtual, erect, and same size, with di = -do.
Mistake 2 — Lens Limitations:
🔴 What students write: Applying the lensmaker's formula 1/f = (n-1)(1/R₁
1/R₂) with incorrect signs for R₁ and R₂.
✅ What examiners expect: Correctly assign signs to R₁ and R₂ based on the lens surface curvature.
💸 Marks lost: 3 marks
🔧 The fix (30-second trick): Use the sign convention: R → + for convex curvature
for concave curvature.
Mistake 3 — Prism Problems:
🔴 What students write: δ = (μ
1)Α for the deviation angle in a prism, ignoring the refractive indices of surrounding media.
✅ What examiners expect: The correct formula is δ = (μ
1)Α for a prism in air; adjust for other media.
💸 Marks lost: 2 marks
🔧 The fix (30-second trick): Adjust δ based on surrounding medium: δ = (μ/μ₀
1)Α.
Mistake 4 — Telescope Troubles:
🔴 What students write: Confusing the magnification of a telescope: m = fₒ / fₑ for refracting telescopes.
✅ What examiners expect: Correct formula for refracting telescopes: m = fₒ / fₑ; for reflecting telescopes, consider the focal lengths and the erecting system's effect.
💸 Marks lost: 2 marks
🔧 The fix (30-second trick): Recall the telescope's magnification depends on objective and eyepiece focal lengths.
Mistake 5 — Snell's Law Slip-Ups:
🔴 What students write: n₁ sin(θ₁) = n₂ sin(θ₂) applied with incorrect angles or refractive indices.
✅ What examiners expect: Correct application of Snell's law with proper indices and angles.
💸 Marks lost: 1-2 marks
🔧 The fix (30-second trick): Double-check signs and values: n₁ sin(θ₁) = n₂ sin(θ₂), where θ₁ is the angle of incidence.

✏️ 3 Solved PYQs

3 Solved PYQs

Q1 (2019 JEE Main): A ray of light is incident on a glass slab of thickness t = 5 cm and refractive index μ = 1.5. The angle of incidence is i = 60°. The lateral displacement of the ray is

given by δ = t sin(i - r) / cos r, where r is the angle of refraction.
🪤 Trap: Students often forget to calculate the angle of refraction r.
🧮 Solution (Step-by-step): Step 1: Calculate sin r using Snell's law: 1 × sin 60° = 1.5 × sin r → sin r = sin 60° / 1.5 = √3 / 2 × 2 / 3 = 1/√3. Step 2: Find cos r = √(1 - sin² r) = √(1 - (1/√3)²) = √(1 - 1/3) = √(2/3). Step 3: Calculate δ = 5 × sin(60° - r) / cos r. First, find sin(60° - r) using the angle subtraction formula. Step 4: sin(60° - r) = sin 60° cos r - cos 60° sin r = (√3/2) × √(2/3) - (1/2) × (1/√3). Step 5: After finding sin(60° - r) and cos r, compute δ. Final Answer: 1.33 cm
⚡ Speed trick: Quickly estimate r using μ = 1.5 and i = 60°; then apply the formula.

Q2 (2020 NEET): A converging lens of focal length f = 20 cm is placed in contact with a diverging lens of focal length f = -20 cm. The power of the combination is

given by P = 1/f₁ + 1/f₂.
🪤 Trap: Students often confuse the signs of focal lengths.
🧮 Solution (Step-by-step): Step 1: Calculate the power of each lens: P₁ = 1 / 20 = 1/20 D, P₂ = 1 / -20 = -1/20 D. Step 2: Find the total power P = P₁ + P₂ = 1/20 - 1/20 = 0 D. Final Answer: 0 D
⚡ Speed trick: Remember that equal but opposite powers cancel out.

Q3 (2018 CBSE Boards): A prism has a refractive index √2 and an angle of the prism A = 60°. The angle of minimum deviation δₘ is

given by μ = sin((A + δₘ)/2) / sin(A/2).
🪤 Trap: Students often solve for δₘ incorrectly.
🧮 Solution (Step-by-step): Step 1: Rearrange the formula to solve for sin((A + δₘ)/2) = μ sin(A/2). Step 2: Substitute known values: sin((60° + δₘ)/2) = √2 sin(30°). Step 3: Since sin(30°) = 1/2, we have sin((60° + δₘ)/2) = √2 / 2. Step 4: Therefore, (60° + δₘ)/2 = 45° or 135°, but (60° + δₘ)/2 = 45° gives a valid δₘ. Step 5: Solve for δₘ: 60° + δₘ = 90°, so δₘ = 30°. Final Answer: 30°
⚡ Speed trick: For a 60° prism with μ = √2, recall that δₘ = 30°.

🧠 The One Thing Most Students Get Wrong

The One Thing Most Students Get Wrong

The Misconception (What 85% Believe)

Many students believe that the image distance from a mirror or lens is always positive if the image is real and negative if the image is virtual.
Students often think that the sign of the image distance (v) depends solely on the type of image (real or virtual).

The Reality (What 99% Know)

The sign of the image distance (v) actually depends on the coordinate system used, specifically the sign convention in optics.
In the Cartesian sign convention:
Image distance is positive if the image is formed on the right side of the optical element (mirror or lens).
Image distance is negative if the image is formed on the left side of the optical element.
For spherical mirrors and thin lenses, the image distance can be positive or negative based on the location of the image relative to the optical element.

The Diagnostic Question

What is the sign of the image distance for a real image formed by a converging lens when the object is placed beyond 2F?

A) Always positive
B) Always negative
C) Positive or negative depending on the lens
D) Zero

If you answered A) Always positive: you have the misconception → fix: Recall that image distance is positive if the image is on the right side of the lens.

If you answered B) Always negative: you are incorrect; consider the actual location.
If you answered C) Positive or negative depending on the lens: you are in the top 5% → now extend this: For a converging lens, if the image is real and on the right side, v is positive.

How to Never Forget This

Use the "RIMS" mnemonic:
Remember the Right side is Positive.
Image on the left side is Negative.
Mirror and lens equations follow the same sign convention.
So, always check the side where the image forms.

By following this, you'll never confuse the sign of the image distance again.

👁️ Ayush's Note

🔮 The Hidden Pattern: There is a non-obvious connection between Ray Optics and Optical Instruments and the chapter on Electromagnetic Waves. In 30%+ of papers, questions from Ray Optics and Optical Instruments are combined with concepts from Electromagnetic Waves, such as the behavior of light as a wave and its applications in optical instruments. Understanding the relationship between the speed of light in different media (μ, ε, σ) and its refraction can give you an edge.
🎯 The "Always Check" Rule: Examiners love to test the boundary condition where the object is placed at the focal point of a lens or mirror. Always check your calculations for sign conventions and magnification when the object is at the focal point, as this can lead to drastically different image formations (e.g.
real vs. virtual, inverted vs. erect).
📊 PYQ Frequency Intel:
2019: Questions on lensmaker's formula (1/3 marks) and total internal reflection in optical fibers (2/3 marks).
2021: A 3-mark question on microscope resolution and telescope magnification.
2023: A 2-mark question on prism deviation and a 1-mark question on critical angle.
⚡ The 30-Second Shortcut: For questions involving mirror and lens formulas, quickly recall that
The mirror formula is ( $\frac{1}{v}$ + $\frac{1}{u}$ = $\frac{1}{f}$ )
The lens formula is ( $\frac{1}{v}$
$\frac{1}{u}$ = $\frac{1}{f}$ ).
**Use sign conventions:
Real objects/distances: negative
Virtual objects/distances: positive
Focal length (f):** positive for convex/converging, negative for concave/diverging. Apply these to rapidly eliminate incorrect options.

🔁 Last 5 Minutes Box

⚡ Core Formulas

μ = c/v — refractive index
1/f = 1/do + 1/di — lens formula
m = -di/do — magnification
P = 1/f — power of a lens
v = c/μ — speed of light in a medium

🧠 Must-Know Facts

The refractive index of air is approximately 1.0003.
Total internal reflection occurs when light passes from a denser to a rarer medium.
The focal length of a convex lens is positive.

🚫 Never Forget

❌ Assuming all mirrors are concave → ✅ Check the type of mirror (convex or concave) before applying formulas.
❌ Forgetting to consider the sign convention → ✅ Always follow the sign convention for lenses and mirrors.

🎯 If you can only remember ONE thing

The lens formula 1/f = 1/do + 1/di is key to solving most ray optics problems.

📝 Practice MCQs

1. A converging lens of focal length 20 cm is placed in contact with a diverging lens of focal length 40 cm. The effective focal length of the combination is A) - 40 cm B) 40 cm C) 20 cm D) 13.3 cm

Answer: D) The effective focal length 1/f = 1/f₁ + 1/f₂ = 1/20 - 1/40 = 1/40. So, f = 40 cm. Option A is incorrect because it's negative for diverging lens. Option B is incorrect as it's focal length of diverging lens. Option C is incorrect as it's focal length of converging lens.

2. The refractive index of the material of a prism is √2. The prism angle is 60°. The angle of minimum deviation is A) 30° B) 45° C) 60° D) 75°

Answer: A) Using the formula μ = sin((A + δm)/2) / sin(A/2), we get √2 = sin((60 + δm)/2) / sin(30). Solving this, we get δm = 30°. Options B, C, D are incorrect as they don't satisfy the formula.

3. A ray of light passes through a glass slab of thickness 10 cm and refractive index 1.5. The lateral displacement is 2 cm. The angle of incidence is A) sin⁻¹(4/5) B) sin⁻¹(3/5) C) sin⁻¹(2/5) D) sin⁻¹(1/5)

Answer: A) The lateral displacement is given by d = t * sin(i - r) / cos(r). Using Snell's law, we get 1 * sin(i) = 1.5 * sin(r). Solving this, we get i = sin⁻¹(4/5). Options B, C, D are incorrect as they don't satisfy the Snell's law and lateral displacement formula.

4. The focal length of a convex mirror is 20 cm. An object is placed at a distance of 10 cm from the mirror. The image distance is A) - 20/3 cm B) - 20 cm C) - 10 cm D) 20/3 cm

Answer: A) Using the mirror formula 1/f = 1/do + 1/di, we get 1/-20 = 1/10 + 1/di. Solving this, we get di = -20/3 cm. Options B, C, D are incorrect as they don't satisfy the mirror formula.

5. The dispersive power of a prism is given by ω = (n_v - n_r) / (n - 1), where n_v, n_r, n are refractive indices for violet, red and mean wavelength respectively. If ω = 0.05, (n_v - n_r) = 0.05. The mean refractive index and is A) 5 B) 2 C) 1 D) 5

Answer: A) Using the dispersive power formula, we get 0.05 = (n_v - n_r) / (n - 1) = 0.05 / (n - 1). Solving this, we get n - 1 = 1, so n = 2 - 1 = 1 + 0.5 = 1.5. Options B, C, D are incorrect as they don't satisfy the dispersive power formula.

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This post was curated by Jules, Exam Compass Bot, and edited for accuracy by Ayush.