Ray optics and optical instruments

NEET

Ray Optics & Optical Instruments

1. Reflection by Spherical Mirrors

Mirror Formula: 1/v + 1/u = 1/f = 2/R.
Magnification: m = hi/ho = -v/u.
f is negative for Concave, positive for Convex.
Concave Mirror Ray Diagram

(Asked in NEET 2018, 2020)

2. Refraction & Lenses

Bending of light when passing from one medium to another.

Snell's Law: μ1 sin i = μ2 sin r.
Apparent Depth: dapp = dreal / μ.
Total Internal Reflection (TIR): Occurs when light moves Denser → Rarer and i > ic (sin ic = 1/μ).
Lens Maker's Formula: 1/f = (μ - 1)(1/R1 - 1/R2).

3. Prism

Angle of Prism A = r1 + r2.
Deviation δ = i + e - A.
Minimum Deviation: δmin occurs when i = e.
μ = sin[(A + δmin)/2] / sin(A/2).
Refraction through Prism

(Asked in NEET 2016, 2017, 2021)

4. Optical Instruments

Simple Microscope: m = 1 + D/f (Near point).
Compound Microscope: m ≈ -(L/fo)(D/fe).
Telescope: m = -fo/fe. Length L = fo + fe.
Compound Microscope

(Asked in NEET 2019, 2022, 2023)

Numericals: Ray Optics

Q1. Object placed 20 cm from concave mirror of focal length 15 cm. Find position and nature of image.
Solution:
u = -20 cm, f = -15 cm.
1/v + 1/u = 1/f
1/v - 1/20 = -1/15
1/v = 1/20 - 1/15 = (3 - 4) / 60 = -1/60.
v = -60 cm. (Real, Inverted, Magnified).
Q2. A pond is 10 m deep. Refractive index of water is 4/3. What is apparent depth?
Solution:
happ = hreal / μ.
happ = 10 / (4/3) = 30/4 = 7.5 m.
Q3. Prism angle 60°, refractive index 1.5. Find angle of minimum deviation.
Solution:
μ = sin[(A + δm)/2] / sin(A/2).
1.5 = sin[(60 + δm)/2] / sin(30).
1.5 × 0.5 = sin[(60 + δm)/2] = 0.75.
sin-1(0.75) ≈ 48.6°.
(60 + δm)/2 = 48.6 → δm = 97.2 - 60 = 37.2°.
Q4. Convex lens radii 20cm and 30cm, μ=1.5. Find focal length.
Solution:
1/f = (μ - 1)(1/R1 - 1/R2).
R1 = +20, R2 = -30.
1/f = (1.5 - 1)(1/20 - 1/(-30)) = 0.5(1/20 + 1/30).
1/f = 0.5(5/60) = 1/2 × 1/12 = 1/24.
f = +24 cm.
Q5. Two lenses of power +10D and -5D are in contact. Find focal length of combination.
Solution:
P = P1 + P2 = 10 - 5 = +5 D.
f = 1/P = 1/5 m = 0.2 m.
f = 20 cm. (Converging).
Q6. Compound microscope has fo = 2cm, fe = 6.25cm. Object at 2.5cm. D=25cm. Magnification?
Solution:
For objective: 1/vo - 1/(-2.5) = 1/2 → 1/vo = 1/2 - 1/2.5 = 1/10. vo = 10 cm.
mo = vo/uo = 10/(-2.5) = -4.
me = 1 + D/fe = 1 + 25/6.25 = 1 + 4 = 5.
M = mo × me = -4 × 5 = -20.
Q7. Find critical angle for glass (μ=1.5) to air interface.
Solution:
sin C = 1/μ = 1/1.5 = 2/3 = 0.666.
C = sin-1(0.666).
C ≈ 41.8°.
Q8. Telescope objective focal length 144 cm, eyepiece 6 cm. Find Magnifying Power.
Solution:
M = -fo / fe.
M = -144 / 6 = -24.
Q9. Speed of light in glass (μ=1.5)? (c = 3 × 108)
Solution:
v = c / μ.
v = 3 × 108 / 1.5.
v = 2 × 108 m/s.
Q10. Equiconvex lens (μ=1.5, R=20cm) has one side silvered. Find equivalent focal length.
Solution:
PL = (μ-1)(2/R) = (0.5)(2/20) = 1/20 cm-1.
PM = -1/(-R/2) = 2/R = 2/20 = 1/10 cm-1 (Concave mirror R/2).
Peq = 2PL + PM = 2(1/20) + 1/10 = 2/10 = 1/5.
Feq = -1/Peq = -5 cm. (Behaves as Concave Mirror).

Important Formulae

1. Reflection (Mirror)

Mirror Formula:

1/v + 1/u = 1/f = 2/R

Magnification:

m = hi/ho = -v/u
2. Refraction & Lenses

Snell's Law:

μ1 sin i = μ2 sin r

Lens Formula:

1/v - 1/u = 1/f

Lens Maker's:

1/f = (μ - 1)(1/R1 - 1/R2)

Power P = 1/f (in meters). For Combination: P = P1 + P2

3. Prism

Prism Formula:

μ = sin[(A + δm)/2] / sin(A/2)

Small Angle Prism:

δ = A(μ - 1)
4. Instruments

Microscope (Compound):

M ≈ (L/fo)(D/fe)

Telescope (Normal Adjustment):

M = -fo/fe | L = fo + fe

20 NEET Golden Facts

  • 1. Focal Length: f = R/2 is valid only for paraxial rays (small aperture).
  • 2. Plane Mirror: Focal length is infinity. Power is zero. Magnification is +1.
  • 3. Refraction: Frequency and Phase do not change. Speed and Wavelength change. (v ∝ λ).
  • 4. TIR Condition: Light must travel from Denser to Rarer medium and i > C.
  • 5. Air Bubble in Water: Behaves like a diverging (concave) lens.
  • 6. Lens in Water: If μlens > μmedium, nature is same, focal length increases (approx 4 times).
  • 7. Invisible Lens: If μlens = μmedium, lens becomes invisible. Focal length becomes infinity.
  • 8. Silvering Lens: Peq = 2PL + PM. Behaves as a Mirror.
  • 9. Dispersion: μV > μR. Deviation δV > δR. Violet bends most.
  • 10. Rainbow: Primary (1 TIR, 2 Refractions, Red top). Secondary (2 TIR, 2 Refractions, Violet top).
  • 11. Scattering: Intensity ∝ 1/λ4 (Rayleigh). Blue sky, Red sunset.
  • 12. Telescope: Large aperture objective used to increase Resolving Power and brightness.
  • 13. Microscope: Objective has small focal length and small aperture. Eyepiece has moderate focal length.
  • 14. Myopia: Short-sightedness. Cannot see far. Corrected by Concave lens.
  • 15. Hypermetropia: Long-sightedness. Cannot see near. Corrected by Convex lens.
  • 16. Critical Angle: Maximum for Red, Minimum for Violet. (sin C = 1/μ).
  • 17. Cutting Lens: Cut vertically → Focal length doubles (2f). Cut horizontally → Focal length same (f).
  • 18. Velocity in Medium: v = c/μ. Denser medium slows down light.
  • 19. Combinations: Equivalent focal length for separated lenses: 1/F = 1/f1 + 1/f2 - d/(f1f2).
  • 20. Optical Path: Distance d in medium μ is equivalent to μd in vacuum.
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