Ray Optics and Optical Instruments — JEE Main Physics Notes & Formulas

1. Chapter at a Glance

Ray optics treats light as rays that travel in straight lines and bend or bounce at surfaces. It covers reflection by plane and spherical mirrors, refraction and total internal reflection, refraction through prisms, lenses and their combinations, and optical instruments (microscope and telescope). This is a heavy-weight JEE Main chapter with one or two questions every year.

What JEE asks most

Mirror and lens formulas with the sign convention; magnification.
Lens maker's formula, lenses in a different medium, combinations.
Prism: minimum deviation, critical angle and total internal reflection.
Magnifying power of microscopes and telescopes.

2. Reflection and Spherical Mirrors

Laws of reflection: angle of incidence = angle of reflection; incident ray, reflected ray and normal lie in one plane.
Plane mirror: image as far behind as the object is in front; rotating the mirror by θ rotates the reflected ray by 2θ.
Sign convention (Cartesian): distances measured from the pole; along the incident light positive, against it negative; heights up positive.
Mirror formula: 1/v + 1/u = 1/f, f = R/2. Magnification m = −v/u.
Concave mirror: real inverted images for objects beyond F; virtual erect magnified image inside F. Convex mirror: always virtual, erect, diminished (used as rear-view mirrors).

3. Refraction and Total Internal Reflection

Snell's law: n₁ sin i = n₂ sin r; n = c/v.
Apparent depth = real depth/n (viewed from above, near-normal). A glass slab of thickness t shifts an object by t(1 − 1/n).
Total internal reflection: when light goes from denser to rarer medium at an angle greater than the critical angle C, with sin C = 1/n. Applications: optical fibres, mirages, sparkling diamonds, totally reflecting prisms.
Refraction at a spherical surface: n₂/v − n₁/u = (n₂ − n₁)/R.

4. Lenses

1/v − 1/u = 1/f m = v/u 1/f = (n − 1)(1/R₁ − 1/R₂) P = 1/f (in m) dioptre

Convex lens: a ray parallel to the axis passes through F after refraction; a ray through the optical centre goes straight on.

Lens in a medium of index n_m: 1/f′ = (n/n_m − 1)(1/R₁ − 1/R₂). A glass lens in water has a longer focal length; in a denser liquid a convex lens can act as diverging.
Thin lenses in contact: 1/F = 1/f₁ + 1/f₂; P = P₁ + P₂.
Silvered lens behaves as a mirror: 1/F = 2/f_lens + 1/f_mirror (plano-convex silvered on the flat side: F = R/2(n − 1); silvered on the curved side: F = R/2n).

5. Prism and Optical Instruments

Prism: r₁ + r₂ = A; deviation δ = i + e − A. At minimum deviation, i = e and r = A/2: n = sin[(A + δ_m)/2]/sin(A/2).
Thin prism: δ = (n − 1)A. Dispersion: violet deviates most because n is larger for shorter wavelengths.
Simple microscope: M = 1 + D/f (image at D = 25 cm) or D/f (image at infinity).
Compound microscope: M = m_o × m_e, with m_o = v_o/u_o and m_e = 1 + D/f_e (near point). Objective and eyepiece both have short focal lengths.
Astronomical telescope: normal adjustment M = f_o/f_e, length f_o + f_e. Large-aperture objectives collect more light and resolve better.

6. Formula Master Table

Quantity	Formula
Mirror	1/v + 1/u = 1/f; m = −v/u
Lens	1/v − 1/u = 1/f; m = v/u
Lens maker	1/f = (n − 1)(1/R₁ − 1/R₂)
Combination	P = P₁ + P₂
Critical angle	sin C = 1/n
Apparent depth / slab shift	d/n; t(1 − 1/n)
Prism	n = sin((A + δ_m)/2)/sin(A/2)
Telescope	M = f_o/f_e

7. Mind Map

Ray Optics

Reflection

Plane, spherical mirrors
Sign convention

Refraction

Snell's law
Apparent depth
TIR

Lenses

Lens formula
Lens maker
Combinations

Prism & instruments

Minimum deviation
Dispersion
Microscope, telescope

8. Tips and Tricks

Shortcuts

Write the sign of every distance before substituting; a real object always has negative u.
Minimum distance between an object and its real image by a convex lens is 4f.
Cutting a lens along its axis (into two halves top and bottom) keeps f the same; cutting it into two plano-convex halves doubles f.
If a lens changes medium, only the (n − 1) factor changes.

Mistakes students make

Using the mirror formula for lenses (the sign between 1/v and 1/u differs).
Forgetting to convert focal length to metres when finding power.
Applying TIR when light goes from a rarer to a denser medium.

9. Important One-liners

A convex mirror always forms a virtual, erect and diminished image.
Optical fibres work on total internal reflection.
Violet light deviates most in a prism; red the least.
Power of a concave lens is negative.
A telescope's resolving power improves with a larger objective aperture.
The focal length of a spherical mirror does not depend on the medium.

10. Solved Numericals: Average to Advanced

Five average-level and five advanced-level problems. Click to reveal each answer and its full working. Use the Cartesian sign convention.

Average level

N1Average

An object is 30 cm in front of a concave mirror of focal length 15 cm. Find the image position and magnification.

Show answer & solution

Concept: 1/v + 1/u = 1/f with u = −30, f = −15.

1/v = 1/f − 1/u = −1/15 + 1/30 = −1/30.
v = −30 cm (real, at the centre of curvature).
m = −v/u = −(−30)/(−30) = −1 (inverted, same size).

Answer: 30 cm in front; m = −1

N2Average

A coin lies at the bottom of a 12 cm deep tank of water (n = 4/3). How deep does it appear from above?

Show answer & solution

Concept: apparent depth = real depth/n.

Apparent depth = 12/(4/3) = 9 cm.
The coin seems raised by 3 cm.

Answer: 9 cm

N3Average

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

Show answer & solution

Concept: 1/v − 1/u = 1/f with u = −30, f = +20.

1/v = 1/20 + 1/(−30) = 1/20 − 1/30 = 1/60.
v = +60 cm (real, on the other side).
m = v/u = 60/(−30) = −2 (inverted, twice as large).

Answer: 60 cm behind the lens; m = −2

N4Average

A convex lens of focal length 20 cm is in contact with a concave lens of focal length 30 cm. Find the focal length and power of the combination.

Show answer & solution

Concept: 1/F = 1/f₁ + 1/f₂.

1/F = 1/20 − 1/30 = 1/60 ⇒ F = +60 cm (converging).
P = 1/0.6 m ≈ +1.67 D.

Answer: 60 cm; about +1.67 D

N5Average

Find the critical angle for light going from glass (n = 1.5) into air.

Show answer & solution

Concept: sin C = 1/n.

sin C = 1/1.5 ≈ 0.667.
C ≈ 41.8°.

Answer: about 41.8°

Advanced level

N6Advanced

A biconvex lens (n = 1.5) has both radii 20 cm. Find its focal length in air and in water (n = 4/3).

Show answer & solution

Concept: lens maker's formula with relative index n/n_m; R₁ = +20, R₂ = −20.

(1/R₁ − 1/R₂) = 1/20 + 1/20 = 1/10.
Air: 1/f = 0.5 × 1/10 ⇒ f = 20 cm.
Water: relative index = 1.5/(4/3) = 1.125 ⇒ 1/f′ = 0.125 × 1/10.
f′ = 80 cm (four times longer).

Answer: 20 cm; 80 cm

N7Advanced

A prism with refracting angle 60° gives a minimum deviation of 30°. Find its refractive index and the critical angle of its material.

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Concept: n = sin[(A + δ_m)/2]/sin(A/2).

(A + δ_m)/2 = 45°; A/2 = 30°.
n = sin45°/sin30° = 0.707/0.5 = √2 ≈ 1.414.
sin C = 1/√2 ⇒ C = 45°.

Answer: √2; 45°

N8Advanced

An astronomical telescope has an objective of focal length 100 cm and an eyepiece of 5 cm. Find its magnifying power and length in normal adjustment. What is its magnifying power when the final image is at 25 cm?

Show answer & solution

Concept: normal adjustment M = f_o/f_e, L = f_o + f_e; near-point M = (f_o/f_e)(1 + f_e/D).

M = 100/5 = 20; L = 105 cm.
Near point: M = 20 × (1 + 5/25) = 20 × 1.2 = 24.

Answer: 20 and 105 cm; 24

N9Advanced

A compound microscope has f_o = 1 cm and f_e = 5 cm. An object is placed 1.1 cm from the objective and the final image forms at 25 cm. Find the magnifying power and the separation of the lenses.

Show answer & solution

Concept: objective forms a real image; the eyepiece magnifies it with m_e = 1 + D/f_e.

Objective: 1/v_o = 1/1 + 1/(−1.1) = 0.0909 ⇒ v_o = 11 cm; m_o = 11/(−1.1) = −10.
Eyepiece: m_e = 1 + 25/5 = 6 ⇒ M = −60 (magnitude 60).
For the eyepiece, v = −25: 1/u_e = 1/v − 1/f = −1/25 − 1/5 = −6/25 ⇒ u_e ≈ −4.17 cm.
Separation = 11 + 4.17 ≈ 15.2 cm.

Answer: 60; about 15.2 cm

N10Advanced

A plano-convex lens (n = 1.5, curved surface radius 30 cm) is silvered on its flat side. Find the focal length of the resulting mirror system.

Show answer & solution

Concept: light passes through the lens twice and reflects once: 1/F = 2/f_L + 1/f_m.

Lens: 1/f_L = (1.5 − 1)(1/30) ⇒ f_L = 60 cm.
Plane mirror: 1/f_m = 0.
1/F = 2/60 ⇒ F = 30 cm; it acts as a concave mirror (check: R/2(n − 1) = 30/1 = 30 cm).

Answer: 30 cm (converging)

11. PYQ-pattern Questions with Solutions

These questions are original and modelled on concepts frequently tested in JEE Main.

Q1Easy

Optical fibres transmit light by:

Refraction
Diffraction
Total internal reflection
Scattering

Show solution

Light keeps hitting the core–cladding boundary at angles above the critical angle.

Answer: (C)

Q2Easy

When white light passes through a prism, the colour deviated most is:

Red
Yellow
Green
Violet

Show solution

Refractive index is largest for violet (shortest wavelength), so it deviates most.

Answer: (D)

Q3Numerical

A lens has a power of −2.5 D. Find its focal length in cm (with sign).

Show solution

f = 1/P = −0.4 m = −40 cm (concave lens).

Answer: −40

Q4Medium

A convex lens is cut into two equal halves by a plane containing its principal axis. The focal length of each half is:

Show solution

Both surfaces (and radii) are unchanged, so f stays the same; only the brightness of the image falls.

Answer: (A)

Q5Hard

The minimum distance between an object and its real image formed by a convex lens of focal length f is:

Show solution

For u = −2f, v = 2f, and the separation 4f is the minimum (it follows from |u| + v ≥ 4f by the AM–GM inequality with 1/|u| + 1/v = 1/f).

Answer: (D)

Q6Numerical

A 6 cm thick glass slab (n = 1.5) is placed over a mark. By how many cm does the mark appear raised?

Show solution

Shift = t(1 − 1/n) = 6 × (1 − 2/3) = 2 cm.

Answer: 2

12. Quick Revision Summary

Remember before the exam

Mirror: 1/v + 1/u = 1/f, m = −v/u; lens: 1/v − 1/u = 1/f, m = v/u.
Lens maker: 1/f = (n − 1)(1/R₁ − 1/R₂); P = P₁ + P₂.
sin C = 1/n; apparent depth d/n; slab shift t(1 − 1/n).
Prism: n = sin((A + δ_m)/2)/sin(A/2); violet deviates most.
Telescope f_o/f_e; microscope m_o × m_e.

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