Q.Derive Prism formula for a prism having angle of prism A and angle of minimum deviation delta_m.
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Dispersion by a Prism – First Principles
Imagine a glass prism — a triangular block. You shine a narrow beam of white light into one face. What comes out the other side is not white. It is a beautiful band of colours: red, orange, yellow, green, blue, indigo, violet — the rainbow. That is dispersion.
Why does this happen? The short answer: different colours of light bend by different amounts when they enter and leave the prism. But the real question is why they bend differently.
The core idea: refractive index depends on colour
When light passes from air into glass, it slows down. The ratio of the speed of light in vacuum to its speed in the material is called the refractive index (n). For a given material, n is not a single number — it changes with the colour (wavelength) of light.
Violet light has the shortest wavelength. It interacts more strongly with the glass molecules, so it slows down the most. That means violet has the highest refractive index in glass. Red light has the longest wavelength, slows down the least, and has the lowest refractive index.
nviolet>nred(for ordinary glass)
Now, when light enters a prism at an angle, it bends according to Snell's law:
n1sinθ1=n2sinθ2
A larger n2 (for violet) means a smaller sinθ2 — so violet bends more toward the normal inside the prism. Red bends less. The same thing happens again when the light exits the other face. The net effect: each colour emerges at a slightly different angle.
The precise statement
Dispersion is the phenomenon in which the refractive index of a medium depends on the wavelength of light, causing different colours to deviate by different amounts when passing through a prism. White light, being a mixture of all visible wavelengths, is thus separated into its constituent colours.
The angle of deviation δ for a colour is given (for a thin prism of small angle A) by:
δ=(n−1)A
Since n is different for each colour, δ is different. Violet deviates the most, red the least.
Dispersion is not the same as refraction. Refraction is the bending of light when it changes medium. Dispersion is the spreading of light into colours because the amount of bending depends on colour. Refraction is the cause; dispersion is the consequence.
A mental picture
Think of a prism as a colour-sorting machine. White light enters as a single beam. Inside the glass, each colour travels at its own speed. Violet, the slowest, takes the sharpest turn. Red, the fastest, takes the gentlest turn. When they exit, they are no longer overlapping — they spread out into a fan of colours. …
The prism formula is n = sin[(A + delta_m)/2] / sin(A/2), derived from the symmetric ray path at minimum deviation.
Let a ray refract through a prism of refracting angle A. At the two faces let the angles be: incidence i, emergence e, and internal refraction angles r1 and r2.
Geometry relations:
- The two internal angles add to the prism angle: r1 + r2 = A.
- The deviation is delta = (i - r1) + (e - r2) = i + e - A.
Condition of minimum deviation: Experiment (and symmetry) show deviation is least when the ray passes symmetrically, i.e. i = e and r1 = r2 = r. Then:
- r1 + r2 = A gives 2r = A, so r = A/2.
- delta = i + e - A becomes delta_m = 2i - A, so i = (A + delta_m)/2. …
Showing the 12 most recent of 36 on this concept.
- CBSE 2026Set A1 markMCQQ.The ratio of the refractive index of red light to blue light in air is (A) less than unity (B) greater than unity (C) equal to unity (D) none of these
›Reveal solutionSolution
Because refractive index rises from red to blue (dispersion), n_red < n_blue, so their ratio is less than 1.
Dispersion arises because the refractive index of a medium depends on wavelength: it is larger for shorter wavelengths (blue) and smaller for longer wavelengths (red). Thus nred<nblue, and their ratio is
…
- CBSE 2026Set ANNUAL1 markMCQQ.The focal length of a lens is minimum for which colour?(a) Red(b) Yellow(c) Violet(d) Blue
›Reveal solutionSolution
Since refractive index decreases from violet to red (dispersion), and f∝1/(μ−1), the colour with the highest μ — violet — bends most and has the smallest focal length.
For a thin lens, the lens-maker's formula gives f1=(μ−1)(R11−R21), so f∝μ−11: a larger refractive index means a smaller focal length. Because the refractive index of ordinary glass is greater for shorter wavelengths, the order from lowest to highest μ across the visible spectrum is red < orange < yellow < green < blue < …
- CBSE 2026Set ANNUAL1 markMCQQ.The speed of light in an isotropic medium depends on :(a) the nature of propagation(b) its intensity(c) the motion of the source with respect to medium(d) its wavelength
›Reveal solutionSolution
A medium's refractive index (and hence the speed of light within it) varies with wavelength -- the phenomenon of dispersion.
Working
The speed of light in a medium is v=c/n. For any real (non-vacuum) isotropic medium, the refractive index n is not fixed but depends on the wavelength of the light (e.g., violet light travels slightly slower than red light in glass) -- this dependence is the cause of dispersion (splitting of white light by a prism).
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- CBSE 2025Set ANNUAL1 markMCQQ.In glass, the velocity of the light is minimum for :(a) red(b) violet(c) yellow(d) green
›Reveal solutionSolution
Violet light bends the most and travels slowest in glass because glass has its highest refractive index for violet light.
Speed of light in a medium is v=c/n. Due to dispersion, the refractive index of glass is different for different colours and increases from red to violet (violet has the shortest wavelength and is refracted most). Since nviolet is the largest …
- CBSE 2025Set ANNUAL1 markMCQQ.If red light and violet rays are of focal lengths f_r and f_v, then which one of the following is true ?(a) lambda_r <= lambda_v(b) lambda_r = lambda_v(c) mu_r > mu_v(d) mu_r < mu_v
›Reveal solutionSolution
Violet light has a shorter wavelength and is refracted more, so its refractive index is higher than red light's.
By Cauchy's dispersion relation, the refractive index of a medium decreases as wavelength increases: μ=A+λ2B (approximately). Since red light has a longer wavelength than violet light (λr>λv), red light is refracted less and has a smaller refractive index than violet light.
…
- CBSE 2025Set ANNUAL1 markMCQQ.If the refractive index of a material of equilateral prism is sqrt(3), then the angle of minimum deviation is(i) 30 degrees(ii) 45 degrees(iii) 60 degrees(iv) 75 degrees
›Reveal solutionSolution
Dm = 60 degrees for an equilateral prism with mu = sqrt(3).
The prism formula is μ=sin(2A)sin(2A+Dm). For an equilateral prism A=60∘, so sin(A/2)=sin30∘=0.5. Then …
- CBSE 2024Set FS1 markMCQQ.The maximum focal length of convex lens is for:(i) blue light(ii) green light(iii) red light(iv) yellow light
›Reveal solutionSolution
f1∝(n−1); red light has the least refractive index in glass, so it gives the greatest focal length — option (iii).
Concept. For a lens, f1=(n−1)(R11−R21), so f is largest when the refractive index n is smallest.
…
- CBSE 2024Set A1 markMCQQ.The wavelength of which colour is minimum? (A) Violet (B) Yellow (C) Blue (D) Red
›Reveal solutionSolution
Violet has the minimum wavelength in the visible spectrum.
In the visible spectrum (VIBGYOR), wavelength increases steadily from violet to red:
Violet(∼400nm)<Blue<Yellow<Red(∼700nm).
…
- CBSE 2024Set A1 markMCQQ.Which causes the formation of rainbow? (A) Diffraction (B) Scattering (C) Refraction (D) Dispersion
›Reveal solutionSolution
A rainbow is produced by dispersion of sunlight inside raindrops → option (D).
When white sunlight enters a spherical raindrop, it refracts, undergoes total internal reflection at the back of the drop, and refracts again as it leaves. Because the refractive index of water is slightly different for each colour (violet bends most, red least), the white light is separated into its constituent colours. This splitting of white light into it …
- CBSE 2024Set ANNUAL1 markMCQQ.With increase in wavelength, the value of refractive index(a) increases(b) decreases(c) remains unchanged(d) none of these
›Reveal solutionSolution
In ordinary transparent media, the refractive index falls off with increasing wavelength - this normal dispersion is why a prism spreads white light into a spectrum with violet deviating most and red least.
For most transparent materials in the visible range, the refractive index depends on wavelength approximately as (Cauchy's empirical formula):
n(λ)=A+λ2B+…
…
- CBSE 2024Set ANNUAL1 markMCQQ.Read the following statements carefully : Assertion (A) : When a narrow beam of white light passes through a glass prism, it undergoes dispersion. Reason (R) : The refractive index of medium for different wavelengths (colours) is different. Select the correct answer from the options given below :(a) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).(b) Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of Assertion (A).(c) Assertion (A) is true, but Reason (R) is false.(d) Both Assertion (A) and Reason (R) are false.
›Reveal solutionSolution
Dispersion happens precisely BECAUSE the prism's refractive index is different for different colours — Reason directly explains Assertion.
Assertion (A): When white light passes through a glass prism, it splits into its constituent colours (dispersion) — this is a well-established, true fact (seen as a rainbow-like spectrum emerging from the prism).
…
- CBSE 2024Set ANNUAL1 markMCQQ.A short pulse of white light is incident from air to a glass slab at normal incidence. After travelling through the glass slab, the first colour to emerge is :(a) blue(b) green(c) violet(d) red
›Reveal solutionSolution
Red light has the lowest refractive index in glass among visible colours, so it travels fastest through the slab and exits first.
The refractive index of glass is different for each colour (wavelength) of light — this is dispersion. Violet light has the shortest wavelength and the highest refractive index in glass, while red light has the longest wavelength and the lowest refractive index (by Cauchy's relation, n decreases as λ increases).
…
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