NEET UG Physics · Chapter 20

Ray Optics and Optical Instruments

Mirrors, refraction, total internal reflection, lenses, prism, microscope and telescope.

NCERT Class 12NEET: 2–3 Qs per paper 14 min read

1. Chapter at a Glance

Ray optics treats light as rays that travel in straight lines. With this simple picture we can explain reflection by mirrors, refraction by lenses and prisms, total internal reflection, and the working of microscopes and telescopes. This is one of the heaviest chapters in NEET Physics: expect two or three questions, many of them numerical, on mirror and lens formulas, lens combinations, prisms and optical instruments.

What NEET asks most
  • Mirror and lens formulas with the correct sign convention.
  • Refractive index, apparent depth and critical angle.
  • Lens maker's formula, power, and lenses in contact.
  • Minimum deviation through a prism.
  • Magnifying power of microscopes and telescopes.

2. Reflection and Spherical Mirrors

1/v + 1/u = 1/f    f = R/2    m = −v/u = h′/h
  • Sign convention (Cartesian): measure all distances from the pole. Distances in the direction of the incident light are positive; distances against it are negative. Heights above the axis are positive.
  • With light coming from the left, a real object has u negative. A concave mirror has f negative; a convex mirror has f positive.
  • A negative m means a real, inverted image; a positive m means a virtual, erect image.
  • A convex mirror always gives a virtual, erect, diminished image (used as a rear-view mirror).

3. Refraction and Total Internal Reflection

Snell's law: n₁ sin i = n₂ sin r    n = c/v    apparent depth = real depth/n
  • Light bends towards the normal when it enters a denser medium (larger n).
  • An object under water appears raised by d(1 − 1/n).
  • Total internal reflection (TIR) occurs when light goes from a denser to a rarer medium and the angle of incidence exceeds the critical angle C, where sin C = 1/n (into air).
  • Uses of TIR: optical fibres, the sparkle of diamonds (C ≈ 24°), mirages, and totally reflecting prisms in binoculars.
Refraction at a spherical surface: n₂/v − n₁/u = (n₂ − n₁)/R

4. Thin Lenses

1/v − 1/u = 1/f    m = v/u    lens maker: 1/f = (n − 1)(1/R₁ − 1/R₂)    P = 1/f (m)
  • A convex (converging) lens has f positive; a concave (diverging) lens has f negative.
  • Power is measured in dioptres (D); f must be in metres.
  • Lenses in contact: 1/F = 1/f₁ + 1/f₂, P = P₁ + P₂.
  • In a medium of index nm, replace (n − 1) with (n/nm − 1). A glass lens has a longer focal length in water; an air bubble in water behaves as a diverging lens.
FF2F2F objectimage
An object between F and 2F of a convex lens (u = −1.5f) gives a real, inverted image at v = 3f, magnified 2 times. The ray parallel to the axis passes through F; the ray through the optical centre goes straight on.

5. Refraction through a Prism

r₁ + r₂ = A    δ = i + e − A    n = sin[(A + δm)/2] / sin(A/2)
  • At minimum deviation, i = e and r₁ = r₂ = A/2; the ray passes symmetrically through the prism.
  • For a thin prism (small A), δ = (n − 1)A.
  • White light splits into colours (dispersion) because n is larger for violet than for red, so violet deviates most.

6. Optical Instruments

InstrumentMagnifying powerNEET Note
Simple microscope (image at D)m = 1 + D/fD = 25 cm; image at infinity gives D/f
Compound microscope (image at D)M = mo × (1 + D/fe)Both fo and fe small; fo < fe
Compound microscope (approx., image at ∞)M ≈ (L/fo)(D/fe)L = tube length
Astronomical telescope (normal adjustment)M = fo/feLength = fo + fe
Telescope (final image at D)M = (fo/fe)(1 + fe/D)Large-aperture objective gathers more light

Reflecting telescopes (Cassegrain type) use a concave mirror as the objective. They have no chromatic aberration, and large mirrors are easier to support than large lenses.

7. Formula Master Table

QuantityFormula
Mirror formula1/v + 1/u = 1/f ; f = R/2
Mirror magnificationm = −v/u
Snell's lawn₁ sin i = n₂ sin r
Critical anglesin C = 1/n
Apparent depthd′ = d/n
Spherical surfacen₂/v − n₁/u = (n₂ − n₁)/R
Lens formula1/v − 1/u = 1/f ; m = v/u
Lens maker's formula1/f = (n − 1)(1/R₁ − 1/R₂)
Power / combinationP = 1/f ; P = P₁ + P₂
Prismn = sin[(A + δm)/2]/sin(A/2)
Thin prismδ = (n − 1)A
TelescopeM = fo/fe

8. Master Summary Table

TopicKey ideaNEET Note
Sign conventionFrom the pole / optical centreMost errors come from signs
Concave mirrorCan form real or virtual imagesVirtual only when object inside F
Convex mirrorAlways virtual, diminishedWide field of view
TIRDenser → rarer, i > COptical fibres, diamond
Lens in waterf increasesUse n/nm
PrismMinimum deviation: i = er = A/2
MicroscopeSmall fo and feMagnifies near objects
TelescopeLarge fo, small feM = fo/fe

9. Mind Map

Ray Optics
Reflection
  • Mirror formula
  • f = R/2
  • m = −v/u
Refraction
  • Snell's law
  • Apparent depth
  • TIR
Lenses and prism
  • Lens maker
  • Power
  • Minimum deviation
Instruments
  • Microscopes
  • Telescopes

10. Tips and Tricks

Shortcuts
  • Object at 2F of a convex lens or at C of a concave mirror: image at the same distance on the other side, same size, inverted.
  • A lens cut in half along the principal axis keeps its focal length; one cut perpendicular to the axis doubles the focal length of each half.
  • Covering half a lens does not cut the image in half; it only makes the image dimmer.
  • For a lens used as a magnifier, the object must be inside F.
Common NEET traps
  • Using the mirror formula sign (1/v + 1/u) for lenses (1/v − 1/u).
  • Forgetting to convert f to metres before finding power in dioptres.
  • Thinking TIR can happen when light goes from air into glass.
  • Mixing up objective and eyepiece focal lengths in telescopes.

11. Important One-liners

  • The focal length of a spherical mirror does not depend on the medium it is in.
  • The focal length of a lens depends on the medium around it.
  • Diamond sparkles because of its small critical angle (about 24°).
  • Optical fibres carry light by repeated total internal reflection.
  • Violet light deviates more than red light in a prism.
  • The least distance of distinct vision is 25 cm for a normal eye.
  • An astronomical telescope gives an inverted final image.
  • A convex mirror is used as a rear-view mirror because it gives a wide field of view.

12. Solved Numericals: Average to Advanced

Five average and five advanced numericals. Use the Cartesian sign convention with light travelling from left to right. Click to reveal each answer and working.

Average level

N1Average

An object is placed 25 cm in front of a concave mirror of focal length 15 cm. Find the position and nature of the image and the magnification.

Show answer & solution

Given: u = −25 cm, f = −15 cm. Concept: 1/v + 1/u = 1/f.

  1. 1/v = 1/f − 1/u = −1/15 + 1/25 = (−5 + 3)/75 = −2/75.
  2. v = −37.5 cm (in front of the mirror, so real).
  3. m = −v/u = −(−37.5)/(−25) = −1.5: inverted and 1.5 times larger.

Answer: 37.5 cm in front of the mirror; real, inverted; m = −1.5

N2Average

A coin lies at the bottom of a tank filled with water (n = 4/3) to a depth of 18 cm. How deep does the coin appear when viewed from directly above, and by how much does it seem raised?

Show answer & solution

Concept: apparent depth = real depth/n.

  1. Apparent depth = 18/(4/3) = 13.5 cm.
  2. Apparent rise = 18 − 13.5 = 4.5 cm.

Answer: 13.5 cm; raised by 4.5 cm

N3Average

Diamond has a refractive index of 2.42. Find its critical angle for light going from diamond into air.

Show answer & solution

Concept: sin C = 1/n.

  1. sin C = 1/2.42 ≈ 0.413.
  2. C ≈ 24.4°. Light entering a well-cut diamond is reflected many times inside, which makes it sparkle.

Answer: about 24.4°

N4Average

An object is 20 cm from a convex lens of focal length 15 cm. Find the image position and magnification.

Show answer & solution

Given: u = −20 cm, f = +15 cm. Concept: 1/v − 1/u = 1/f.

  1. 1/v = 1/15 + 1/(−20) = (4 − 3)/60 = 1/60.
  2. v = +60 cm (real, on the other side).
  3. m = v/u = 60/(−20) = −3 (inverted, 3 times larger).

Answer: 60 cm behind the lens; m = −3

N5Average

A convex lens of focal length 25 cm is in contact with a concave lens of focal length 50 cm. Find the power and focal length of the combination.

Show answer & solution

Concept: P = P₁ + P₂ with f in metres.

  1. P₁ = 1/0.25 = +4 D; P₂ = 1/(−0.5) = −2 D.
  2. P = +2 D.
  3. F = 1/P = 0.5 m = 50 cm (converging).

Answer: +2 D; 50 cm (converging)

Advanced level

N6Advanced

A biconvex lens of glass (n = 1.6) has both radii of curvature equal to 30 cm. Find its focal length in air and in water (n = 4/3).

Show answer & solution

Given: R₁ = +30 cm, R₂ = −30 cm. Concept: lens maker's formula.

  1. In air: 1/f = (1.6 − 1)(1/30 + 1/30) = 0.6 × 2/30 = 0.04 ⇒ f = 25 cm.
  2. In water: relative index = 1.6/(4/3) = 1.2 ⇒ 1/f = 0.2 × 2/30 = 1/75.
  3. f = 75 cm (three times longer in water).

Answer: 25 cm in air; 75 cm in water

N7Advanced

An equilateral prism (A = 60°) is made of glass of refractive index √3. Find its angle of minimum deviation and the angle of incidence at that position.

Show answer & solution

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

  1. sin[(60° + δm)/2] = √3 × sin 30° = √3/2.
  2. (60° + δm)/2 = 60° ⇒ δm = 60°.
  3. At minimum deviation, i = (A + δm)/2 = 60°, and r = A/2 = 30°.

Answer: δm = 60°; i = 60°

N8Advanced

A compound microscope has an objective of focal length 2 cm and an eyepiece of focal length 6.25 cm. An object is placed 2.5 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: M = mo(1 + D/fe).

  1. Objective: 1/vo = 1/2 + 1/(−2.5) = 0.1 ⇒ vo = 10 cm; mo = 10/(−2.5) = −4.
  2. Eyepiece: me = 1 + 25/6.25 = 5; M = −4 × 5 = −20.
  3. Eyepiece object distance: 1/ue = 1/(−25) − 1/6.25 = −0.2 ⇒ ue = −5 cm.
  4. Separation = vo + |ue| = 10 + 5 = 15 cm.

Answer: magnifying power 20 (image inverted); separation 15 cm

N9Advanced

An astronomical telescope has an objective of focal length 150 cm and an eyepiece of 5 cm. Find its magnifying power and length (a) in normal adjustment, (b) when the final image forms at 25 cm.

Show answer & solution

Concept: normal adjustment M = fo/fe; near point M = (fo/fe)(1 + fe/D).

  1. (a) M = 150/5 = 30; length = 150 + 5 = 155 cm.
  2. (b) M = 30 × (1 + 5/25) = 36.
  3. Eyepiece object distance: 1/ue = −1/25 − 1/5 = −6/25 ⇒ |ue| ≈ 4.17 cm; length ≈ 154.2 cm.

Answer: (a) 30, 155 cm; (b) 36, about 154 cm

N10Advanced

A point object in air is 30 cm from the convex surface of a long glass rod (n = 1.5) whose end has a radius of curvature of 10 cm. Where is the image formed?

Show answer & solution

Given: n₁ = 1, n₂ = 1.5, u = −30 cm, R = +10 cm. Concept: n₂/v − n₁/u = (n₂ − n₁)/R.

  1. 1.5/v − 1/(−30) = 0.5/10 = 0.05.
  2. 1.5/v = 0.05 − 0.0333 = 0.01667.
  3. v = 1.5/0.01667 = +90 cm (real image inside the glass).

Answer: 90 cm inside the rod (real image)

13. NEET-pattern Questions with Detailed Answers

These questions are original and based on concepts that NEET UG asks again and again.

Q1Easy

The image formed by a convex mirror is always:

  1. Real and inverted
  2. Virtual, erect and diminished
  3. Virtual and magnified
  4. Real and magnified
Show solution

For any real object, a convex mirror gives a virtual, erect and smaller image behind the mirror. Magnified virtual images come from a concave mirror with the object inside F.

Answer: (B)

Q2Easy

Total internal reflection can occur when light travels from:

  1. Air to water
  2. Air to glass
  3. Glass to air
  4. Water to glass
Show solution

TIR requires light to go from a denser to a rarer medium, as from glass to air. In the other three options, light goes into a denser medium.

Answer: (C)

Q3Medium

A convex lens of focal length 20 cm is placed in contact with a concave lens of focal length 20 cm. The combination behaves as:

  1. A convex lens of f = 10 cm
  2. A concave lens of f = 10 cm
  3. A plane glass plate
  4. A convex lens of f = 40 cm
Show solution

P = +5 − 5 = 0, so the focal length is infinite. The combination behaves like a plane glass plate and neither converges nor diverges light.

Answer: (C)

Q4Medium

When a glass lens is immersed in water, its focal length:

  1. Decreases
  2. Increases
  3. Stays the same
  4. Becomes zero
Show solution

The relative refractive index ng/nw is smaller than ng, so (n − 1) falls and f increases. A mirror's focal length would not change.

Answer: (B)

Q5Medium

At minimum deviation through a prism:

  1. The angle of incidence is 90°
  2. The ray inside the prism is parallel to its base (for an isosceles prism)
  3. The angle of emergence is zero
  4. The deviation equals the prism angle
Show solution

At minimum deviation, i = e and r₁ = r₂. The ray passes symmetrically through the prism, so for an isosceles prism it is parallel to the base. (D) is only a special case, such as N7 above.

Answer: (B)

Q6Medium

The magnifying power of an astronomical telescope in normal adjustment is 24, and the length of its tube is 125 cm. The focal lengths of the objective and eyepiece are:

  1. 120 cm and 5 cm
  2. 5 cm and 120 cm
  3. 100 cm and 25 cm
  4. 115 cm and 10 cm
Show solution

We need fo/fe = 24 and fo + fe = 125. This gives 25fe = 125, so fe = 5 cm and fo = 120 cm. (B) swaps the two lenses.

Answer: (A)

Q7Hard

An air bubble inside a glass slab behaves like a:

  1. Converging lens
  2. Diverging lens
  3. Plane glass plate
  4. Concave mirror
Show solution

The bubble is convex in shape, but its index (1) is less than the surrounding glass (1.5). So nrel − 1 is negative and it diverges light. A convex shape converges only if it is denser than its surroundings.

Answer: (B)

Q8Hard

The lower half of a convex lens is covered with black paper. The image of an object:

  1. Shows only the upper half of the object
  2. Shows only the lower half
  3. Is complete but less bright
  4. Is not formed
Show solution

Every part of the lens receives rays from every point of the object, so the full image still forms. Only half as much light reaches it, so the image is dimmer.

Answer: (C)

14. 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.
  • n = c/v; sin C = 1/n; apparent depth = d/n.
  • Lens maker 1/f = (n − 1)(1/R₁ − 1/R₂); P = 1/f; P adds in contact.
  • Prism: n = sin[(A + δm)/2]/sin(A/2); thin prism δ = (n − 1)A.
  • Microscope M = mo(1 + D/fe); telescope M = fo/fe.
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