Optics — Mirrors, Lenses, Interference and the Electromagnetic Spectrum
1/v − 1/u = 1/f for lenses and 1/v + 1/u = 1/f for mirrors are two substitutions rather than two puzzles. Wave optics then adds one idea — path difference — from which the double-slit fringe width, the condition for a dark band and the width of a diffraction maximum all follow. The electromagnetic spectrum closes the chapter, and it is asked as an ordering.Wave Optics: One Idea, Three Results
Everything here is path difference. Two coherent sources reinforce where the path difference is a whole number of wavelengths and cancel where it is an odd number of half-wavelengths, and in Young's experiment that gives fringes of width β = λD/d — so the fringes widen with a longer wavelength or a bigger screen distance, and narrow if the slits are moved apart. Three consequences the paper asks: immersing the apparatus in water shrinks the fringe width, because λ falls; white light gives a white central fringe with coloured edges, because every wavelength has zero path difference at the centre; and single-slit diffraction gives a central maximum of angular width 2λ/a, which is wider for a narrower slit.
- Interference needs coherence. Two independent bulbs give no fringes however identical, which is why one slit is split into two — and why a laser makes the experiment easy.
- Polarisation proves light is transverse, and nothing else in the syllabus does. Sound cannot be polarised, and that contrast is the question.
- Brewster: at the polarising angle
tan θ_p = n, the reflected light is completely polarised, and the reflected and refracted rays are then perpendicular. - The blue sky is Rayleigh scattering, which goes as 1/λ⁴ — so blue scatters far more than red, and the setting sun is red because the blue has been scattered out of the long path.
β = λD/d). Widen a single slit and the diffraction maximum also gets narrower (2λ/a). But narrow the single slit and the pattern spreads — which is the counter-intuitive direction and the one CUET sets. The distinguishing fact if a question asks how to tell the two patterns apart: interference fringes are of equal width and equal intensity, while a diffraction pattern has a bright central maximum with rapidly fainter maxima on either side.Electromagnetic Waves, in the Two Questions They Get
An electromagnetic wave carries E and B perpendicular to each other and both perpendicular to the direction of travel, in phase, with E₀/B₀ = c and c = 1/√(μ₀ε₀). It needs no medium. Maxwell's addition to Ampère's law was the displacement current ε₀ dφ_E/dt, which is what flows "through" the gap of a charging capacitor and makes the total current continuous. The spectrum in increasing frequency — equivalently decreasing wavelength — is radio, microwave, infrared, visible, ultraviolet, X-ray, gamma, and the visible band runs about 400 nm (violet) to 700 nm (red).
Key takeaways
- One sign convention answers most of ray optics: along the incident light is positive. Mirrors take 1/v + 1/u = 1/f with m = −v/u; lenses take 1/v − 1/u = 1/f with m = v/u. Power is 1/f in metres, and lenses in contact add powers.
- Total internal reflection needs BOTH denser-to-rarer travel and an angle beyond C = sin⁻¹(1/n). On refraction the frequency never changes, while speed and wavelength both fall in a denser medium.
- Fringe width is β = λD/d, so it grows with wavelength and screen distance and shrinks as the slits separate or the apparatus is immersed. A single slit's central maximum is 2λ/a wide — wider for a narrower slit.
- Polarisation is the proof that light is transverse; Rayleigh scattering goes as 1/λ⁴, which is why the sky is blue and the setting sun red. The spectrum by rising frequency is radio, microwave, infrared, visible, ultraviolet, X-ray, gamma.
Practice questions (8)
Attempt each one before opening the answer. Every explanation names the tempting wrong option as well as the right one, because that is where marks are lost.
The power of a convex lens of focal length 20 cm is:
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Answer: B — +5 D
Power is 1/f with f in metres, so f = 0.20 m gives P = 1/0.20 = +5 D, positive because the lens is convex and converging. The +0.05 D option uses f in centimetres, which is the single commonest error in this item — the dioptre is defined per metre and nothing else. −5 D has the right magnitude and the sign of a concave lens. And +20 D simply reports the focal length in centimetres with dioptres attached, which no formula produces.In Young's double-slit experiment, the fringe width will DECREASE if:
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Answer: B — The separation between the slits is increased
β = λD/d, so d is in the denominator and increasing the slit separation narrows the fringes. Moving the screen farther increases D and therefore widens them. Replacing blue with red increases λ and also widens them, which is why the coloured-light options in this family have to be read for direction rather than recognised. And intensity appears nowhere in the formula: a brighter source gives brighter fringes at exactly the same spacing, which is the distractor that separates candidates using the formula from those reasoning loosely about "more light".Light passes from glass (n = 1.5) into air. Total internal reflection can occur:
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Answer: B — Only when the angle of incidence in the glass exceeds sin⁻¹(1/1.5)
Both conditions must hold, and here the first already does — the light is going from denser to rarer — so what remains is the angle: it must exceed the critical angle sin⁻¹(1/n) = sin⁻¹(0.667), about 42°. "At every angle" keeps the medium condition and forgets the angle, which is the incomplete answer this item is built on. Normal incidence is the case where light passes straight through with no bending at all, the opposite of the situation. And the last option misdescribes the physics: at total internal reflection the light never enters the air, and the reflection happens at the boundary from the glass side.When light travels from air into water, which quantity remains unchanged?
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Answer: B — Frequency
Frequency is set by the source and cannot change at a boundary, so it is the invariant; the speed falls to c/n and the wavelength falls in the same ratio, which is why v = fλ still balances. Speed and wavelength are therefore both wrong, and wavelength is the most-chosen wrong answer because the colour of the light seems unchanged — colour tracks frequency, not wavelength in the medium. Amplitude also changes, since part of the light is reflected at the surface and the transmitted wave carries less energy.Arranged in order of INCREASING frequency, the electromagnetic spectrum is:
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Answer: B — Radio, microwave, infrared, visible, ultraviolet, X-ray, gamma
Radio has the lowest frequency and gamma the highest, with infrared just below the visible band and ultraviolet just above it. The reversed list is the same sequence in order of increasing WAVELENGTH, and it is the answer given by candidates who know the order but not which end the question asks from — reading the word "increasing" against the right quantity is the whole task. The third option swaps infrared with microwave and X-ray with ultraviolet. The fourth is unordered at both ends.The phenomenon that establishes light as a transverse wave is:
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Answer: B — Polarisation
Only a transverse wave can be polarised, because polarisation is a restriction of the vibration to one plane perpendicular to the direction of travel — and sound, being longitudinal, cannot be polarised at all. Interference and diffraction both prove that light is a WAVE, which is a weaker claim, and they are the options a candidate picks who remembers "wave nature" without the transverse part. Refraction is explained perfectly well by both wave and particle pictures and settles nothing about either.A Young's double-slit apparatus is immersed in water. Compared with air, the fringe width:
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Answer: B — Decreases, because the wavelength in water is smaller by the refractive index
β = λD/d depends on the wavelength IN THE MEDIUM, and λ_water = λ_air/n, so the fringe width falls by the same factor n — for water, to about three quarters of its value in air. The slowing of light is the cause of the smaller wavelength, but stated on its own it points the wrong way and is the trap. "Stays the same because the frequency does not change" is a true premise with a false conclusion: the fringe pattern is set by wavelength and path difference, not by frequency. And the last option gets the right direction from an invented mechanism — the apparatus does not contract, which matters because a right answer for a wrong reason will not survive the next version of the question.An object is placed 30 cm in front of a concave mirror of focal length 20 cm. The image is:
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Answer: B — Real, inverted and 60 cm in front of the mirror, magnified two times
With the convention that distances against the incident light are negative, u = −30 and f = −20, so 1/v = 1/f − 1/u = −1/20 + 1/30 = −1/60 and v = −60 cm: 60 cm in front of the mirror, hence real. The magnification m = −v/u = −(−60)/(−30) = −2, so the image is inverted and twice the size — which is the standard result for an object between f and 2f. The virtual option ignores the sign of v. 12 cm comes from adding the reciprocals instead of subtracting. And the image is at infinity only when the object sits exactly at the focus, which 30 cm is not.