Ray optics for NEET

Ray optics is one of the most formula-driven chapters in NEET physics. Nearly every question comes down to the mirror or lens formula, Snell's law, the critical angle or the prism formula. The formulas are simple. The marks go wrong on signs: a focal length entered as positive when it should be negative, or a virtual image read as real.

So this guide starts with the sign convention and returns to it in every example.

Sign convention and the two formulas

NCERT uses the Cartesian sign convention:

• All distances are measured from the pole (mirror) or optical centre (lens).
• Distances in the direction of the incident light are positive; against it, negative. With light travelling left to right, the object distance u is negative for a real object.
• Heights above the principal axis are positive; below, negative.

For a mirror, f = R/2. A negative m means the image is inverted (and, for a single mirror or lens, real). A positive m means erect and virtual.

Where the image forms

For a convex lens (a concave mirror behaves the same way, with the image on the same side as the object):

A convex mirror and a concave lens always form a virtual, erect, diminished image, whatever the object position.

Refraction

• Refractive index: n = c/v. Snell's law: n₁ sin i = n₂ sin r.
• Frequency never changes on refraction. Speed and wavelength fall by the factor n in a denser medium.
• Apparent depth: an object at real depth d in a medium of index n, viewed from above at near-normal incidence, appears at d/n. The apparent rise is d(1 − 1/n). A glass slab of thickness t shifts an object by t(1 − 1/n).

Refraction at a spherical surface: n₂/v − n₁/u = (n₂ − n₁)/R. Apply it twice and you get the lens maker's formula.

Total internal reflection

When light goes from a denser to a rarer medium and the angle of incidence exceeds the critical angle C, all of it reflects back. For light going from a medium of index n into air:

sin C = 1/n

Both conditions are needed: denser to rarer, and i > C.

Applications: optical fibres, the sparkle of a cut diamond, mirages, and totally reflecting prisms that turn light through 90° or 180°.

Lens maker's formula and power

1/f = (n − 1)(1/R₁ − 1/R₂), with R₁ and R₂ signed by the Cartesian convention. For a lens in a medium, replace n with n_lens/n_medium.

• A glass lens (n = 1.5) in water (n = 4/3) has n_rel = 1.125, so (n_rel − 1) falls from 0.5 to 0.125. Its focal length becomes 4 times longer.
• If the medium has a higher index than the lens, a convex lens diverges.

Power: P = 1/f, with f in metres, measured in dioptres (D). Converging lenses have positive power.

For thin lenses in contact: P = P₁ + P₂, and 1/F = 1/f₁ + 1/f₂.

Prism

For a prism of angle A, with incidence angle i, emergence angle e and refraction angles r₁ and r₂:

• r₁ + r₂ = A
• Deviation δ = i + e − A

As i increases, δ first falls, reaches a minimum δ_m, then rises. At minimum deviation, i = e, r₁ = r₂ = A/2, and the ray inside passes symmetrically:

n = sin[(A + δ_m)/2] / sin(A/2)

For a thin prism (small A): δ = (n − 1)A.

Plotting δ against i for a triangular prism is one of the experimental-skills items in the syllabus. Expect a question on the shape of that graph, a U-shaped curve with a single minimum.

Optical instruments

A telescope needs an objective of large focal length and an eyepiece of short focal length. A microscope needs both to be short.

Worked numericals

Example 1: convex lens

A convex lens has f = +20 cm. An object is at u = −30 cm.

• 1/v = 1/f + 1/u = 1/20 − 1/30 = 1/60, so v = +60 cm.
• m = v/u = 60/(−30) = −2. The image is real, inverted and twice the size.

Example 2: concave mirror, object inside F

A concave mirror has f = −15 cm. An object is at u = −10 cm.

• 1/v = 1/f − 1/u = −1/15 + 1/10 = (−2 + 3)/30 = 1/30, so v = +30 cm.
• Positive v means the image is behind the mirror: virtual.
• m = −v/u = −30/(−10) = +3: erect and three times the size. This is how a shaving mirror works.

Example 3: lens maker's formula in air and water

A biconvex lens has R₁ = +20 cm, R₂ = −20 cm and n = 1.5.

• In air: 1/f = 0.5 × (1/20 + 1/20) = 0.5 × 0.1 = 0.05, so f = 20 cm.
• In water (n = 4/3): n_rel = 1.5 × 3/4 = 1.125. 1/f = 0.125 × 0.1 = 0.0125, so f = 80 cm.

Example 4: minimum deviation

A prism of angle 60° gives a minimum deviation of 30°.

• n = sin[(60 + 30)/2] / sin 30° = sin 45°/sin 30° = 0.707/0.5 = √2 ≈ 1.41.

Example 5: apparent depth

A coin lies at the bottom of water 12 cm deep (n = 4/3).

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

Practice MCQs

1. A concave mirror has a radius of curvature of 40 cm. Its focal length is: (a) −10 cm (b) −20 cm (c) −40 cm (d) −80 cm
2. The power of a lens of focal length −25 cm is: (a) +4 D (b) −4 D (c) −0.25 D (d) −25 D
3. The critical angle for a medium of refractive index √2 is: (a) 30° (b) 45° (c) 60° (d) 90°
4. A thin prism of angle 5° and n = 1.5 deviates a ray by: (a) 2.5° (b) 5° (c) 7.5° (d) 10°
5. An object is placed at the focus of a convex lens. The image forms: (a) at the focus (b) at 2F (c) at infinity (d) on the same side
6. Lenses of +5 D and −2 D are placed in contact. The focal length of the combination is about: (a) 14 cm (b) 20 cm (c) 33 cm (d) 50 cm
7. A glass slab 6 cm thick (n = 1.5) is placed over a mark. The mark appears raised by: (a) 1 cm (b) 2 cm (c) 3 cm (d) 4 cm
8. An astronomical telescope has f_o = 100 cm and f_e = 5 cm. In normal adjustment, its magnifying power and tube length are: (a) 20 and 105 cm (b) 20 and 95 cm (c) 500 and 105 cm (d) 5 and 100 cm

Answers

1. (b) f = R/2 = 20 cm, negative for a concave mirror.
2. (b) P = 1/(−0.25 m) = −4 D.
3. (b) sin C = 1/√2.
4. (a) δ = (1.5 − 1) × 5° = 2.5°.
5. (c) 1/v = 1/f + 1/u = 1/f − 1/f = 0.
6. (c) P = +3 D, f = 1/3 m ≈ 33 cm.
7. (b) 6 × (1 − 1/1.5) = 6 × 1/3 = 2 cm.
8. (a) m = 100/5 = 20; length = 100 + 5 = 105 cm.

What to do next

• Write the sign convention on the first line of every optics problem until it becomes automatic.
• Redraw the image-position table from ray diagrams, not from memory.
• Solve ten mirror and lens problems, checking each answer against the table (real or virtual, magnified or diminished).
• Practise five prism questions, including one on the δ–i graph.
• Move on to wave optics for NEET, which explains what ray optics cannot: interference, diffraction and polarisation.

If sign errors keep costing you marks, see common NEET physics mistakes.