Optics & Light — Part 1: 40 MCQs with Explanations

Magnification m = -v/u = -2 (real image). So v = 2u = 60 cm. Using 1/f = 1/v + 1/u = 1/60 + 1/30 = 3/60 = 1/20. Therefore f = 20 cm.

Balmer series (transitions to n=2) lies in the visible region of electromagnetic spectrum.

Critical angle θ_c = sin⁻¹(1/n) = sin⁻¹(1/1.5) = sin⁻¹(0.667) ≈ 42°.

Dispersion is the splitting of white light into spectrum colors due to wavelength-dependent refractive index.

v = c/n = (3 × 10^8)/1.5 = 2 × 10^8 m/s.

When plane surface is silvered, system behaves as concave mirror with f_mirror = f_lens/2 = 20/2 = 10 cm.

For same size real image, object must be at center of curvature C = 2f = 30 cm.

θ_c = sin⁻¹(1/n) = sin⁻¹(1/2.42) ≈ sin⁻¹(0.413) ≈ 24.4°.

For lenses in contact: 1/f = 1/f₁ + 1/f₂.

Longest λ: n=2→1, 1/λ₁ = R(1 - 1/4) = 3R/4. Shortest λ: n=∞→1, 1/λ₂ = R(1 - 0) = R. Ratio λ₁/λ₂ = R/(3R/4) = 4/3.

Cauchy's equation: n = A + B/λ² + C/λ⁴ describes dispersion (variation of n with λ).

Plane mirror produces virtual image of same size: m = +1 (positive for virtual image).

1/f ∝ (n_lens/n_medium - 1). In air: 1/f_a ∝ (1.5/1 - 1) = 0.5. In water: 1/f_w ∝ (1.5/1.33 - 1) ≈ 0.125. Ratio f_w/f_a = 0.5/0.125 = 4. So f_w = 80 cm.

Refractive index n = c/v, where c is speed of light in vacuum and v is speed of light in the medium. Since c > v, n > 1 for all material media.

According to sign convention in optics, focal length of concave mirror is taken as negative because the focus lies in front of the mirror (in the direction of incident light).

Critical angle is the angle of incidence in the denser medium for which angle of refraction in the rarer medium is 90°. Beyond this angle, total internal reflection occurs.

For image at near point (least distance of distinct vision D): M = 1 + D/f, where f is focal length of convex lens used as magnifier.

Constructive interference (bright fringe) occurs when path difference = nλ, where n = 0, 1, 2,... and λ is wavelength.

Angle of minimum deviation δₘ = (μ-1)A for small angle prisms, where μ is refractive index and A is angle of prism. For larger angles, the relationship is more complex but still depends on both factors.

Resolving power ∝ 1/λ (wavelength). Shorter wavelength (e.g., blue light or electron beams) provides better resolution.

sin C = 1/n = 1/1.5 = 0.6667. C = sin⁻¹(0.6667) ≈ 42°.

Lens maker's formula: 1/f = (μₗ/μₘ - 1)(1/R₁ - 1/R₂). Since μₗ/μₘ decreases when lens is immersed in water (μₘ > 1), focal length increases.

Minimum wavelength λₘᵢₙ = hc/eV, where V is accelerating voltage. It depends only on tube voltage, not on target material.

Total internal reflection occurs when: (i) light travels from denser to rarer medium, and (ii) angle of incidence exceeds critical angle.

Lens formula: 1/f = 1/v - 1/u (using Cartesian sign convention where u is negative for real objects). Many textbooks write it as 1/f = 1/v + 1/u with different sign conventions. The standard form with proper signs is 1/f = 1/v - 1/u.

v = c/n = 3 × 10⁸/2.42 ≈ 1.24 × 10⁸ m/s.

Power P (in diopters) = 1/f (in meters) = 1/0.5 = +2 D. Positive sign indicates converging (convex) lens.

Optical fibers work on principle of total internal reflection, where light is confined within core due to repeated reflections at core-cladding interface.

When plane surface silvered, system behaves as concave mirror with f_mirror = f_lens/2 = 30/2 = 15 cm.

Longest λ: n=3→2, 1/λ₁ = R(1/4 - 1/9) = 5R/36. Shortest λ: n=∞→2, 1/λ₂ = R(1/4 - 0) = R/4. Ratio λ₁/λ₂ = (R/4)/(5R/36) = 9/5.

Plane mirror produces virtual image of same size: m = +1 (positive for virtual image).

1/f ∝ (n_lens/n_medium - 1). In air: 1/f_a ∝ (1.5/1 - 1) = 0.5. In water: 1/f_w ∝ (1.5/1.33 - 1) ≈ 0.125. Ratio f_w/f_a = 0.5/0.125 = 4. So f_w = 100 cm.

Critical angle θ_c = sin⁻¹(1/n). Since n_violet > n_red, θ_c is minimum for violet light.

Covering one slit converts setup to single slit diffraction experiment.

1/f = (n-1)(1/R₁ - 1/R₂), where R₁ and R₂ are radii of curvature of two surfaces (sign convention applies).

When object between P and F of concave mirror, image is virtual, erect, and magnified (used in shaving mirrors).

ₐn_g = 1.5, ʷn_g = 1.125. Since ʷn_g = ₐn_g/ₐn_w ⇒ ₐn_w = ₐn_g/ʷn_g = 1.5/1.125 = 1.33.

Nuclear fusion (e.g., in sun: 4¹H → ⁴He + 2e⁺ + 2ν + energy) releases enormous energy per nucleon compared to fission.

Lyman series (transitions to n=1) has wavelengths 91-122 nm, in ultraviolet region.

Balmer series (transitions to n=2) has wavelengths 365-656 nm, in visible region.