REFRCTION THROUGH PRISM Ray Optics-IV Physics Without Fear
CONTENTS Refraction through a Prism ngle of Deviation Expression for Deviation produced by a Prism Variation of angle of deviation δ with angle of incidence i Expression for Refractive Index of Prism (The Prism Formula) Dispersion ngular Dispersion Dispersive Power
REFRCTION THROUGH PRISM Refraction Through a Prism: i > r1 (On face ) e > r2 (On face C) Emergent ray QE is not parallel to Incident ray OP. The light bends toward the base of the prism through an angle δ; called the angle of deviation. We will derive expression for the angle of deviation and study the factors affecting the same. N N 2 1 P D δ i e Q r 1 r E 2 µ C O REFRCTION THROUGH PRISM OP: Incident ray PQ: Refracted ray QE: Emergent ray δ : ngle of deviation
REFRCTION THROUGH PRISM O 1 N N 2 1 P D δ i e Q r 1 O r 2 µ C Sum of angles of incidence and emergence is equal to the sum of angle of prism and angle of deviation.
EXPRESSION FOR DEVITION O 1 N N 2 1 P D δ i e Q r 1 O r 2 E µ C Hence for small-angled prism and for small angle of incidence; the deviation depends on the angle of prism & the material of the prism.
RECP O 1 N N 2 1 P D δ i e Q r 1 O r 2 µ C Refraction through a prism OP: Incident ray PQ: Refracted ray QE: Emergent ray δ : ngle of deviation
Variation of δ with i VRITION OF NGLE OF DEVITION δ WITH NGLE OF INCIDENCE i : For small i; δ is large. s i increases, δ decreases. In general, for a given δ, there are two values of angle of incidence. t a certain value of angle i, the angle of deviation becomes minimum called ngle of minimum deviation δ m. t this angle; (δ=δ m ) the light passes symmetrically through the prism. Refracted ray PQ C. We have, i = e & r 1 = r 2 = r (say). δ m δ O i 1 i = e i 2 Variation of δ with i fter minimum deviation, angle of deviation δ starts increasing with angle of incidence. The variation is as shown in the graph. i
Refractive Index of Material of Prism Expression for Refractive Index of Material of Prism ccording to Snell s law, sin i sin i µ = = sin r1 sin r µ = sin ( + δ m ) 2 sin 2 The above relation is used to determine the refractive index of the material of the prism.
DISPERSION OF LIGHT Dispersion of Light: It is the phenomenon of splitting of a ray of light into its constituent colours (wavelengths). The band of colours formed is called Spectrum. Rainbow in nature is formed due to dispersion of white light. ray of white light gets dispersed into its constituent colours (wavelengths) appearing as a band of colours from violet to red, called spectrum of white light(vigyor). N D δ v δ r Rainbow White Light C
DISPERSION OF LIGHT R O Y G I White Light The colours may be recombined in an identical inverted prism to reproduce white light as shown above. Cause of Dispersion: The deviation produced by a given prism depends on the refractive index of the material of the prism. Since µ is a function of wavelength or colour of light, different colours get deviated through different colours resulting in dispersion. The same can be explained using Cauchy s equation.
WHY DISPERSION OF LIGHT?
NGULR DISPERSION & DISPERSIVE POWER ngular Dispersion: It is defined as the angle between violet & red emergent rays. Mathematically; it is the difference the deviations suffered by violet and the red rays. ngular dispersion = δ v δ r = {(µ v 1) - (µ r 1)} = (µ v µ r ) Mean Deviation: It is the deviation produced by prism in yellow colour. δ v - δ r N D δ v δ r White Light C
DISPERSIVE POWER δ v - δ r N D δ v δ r White Light C
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