Four transparent media A, B, C and D are arranged in contact so that a light ray…

PHYSICS · Multi-part · CBSE · Physics · Light — Reflection and Refraction · Light — Reflection and Refraction

Problem

Four transparent media A, B, C and D are arranged in contact so that a light ray passes through them in the order A → B → C → D. Known data: • Absolute refractive index of medium A,

n_{A}=1.00

(air). • Relative refractive index of B with respect to A,

n_{BA}=1.30

. • Relative refractive index of C with respect to B,

n_{CB}=\dfrac{5}{4}

. • Relative refractive index of D with respect to C,

n_{DC}=1.10

. (i) Express the absolute refractive index of medium D,

n_{D}

, in terms of

n_{A}

and the three given relative refractive indices. (ii) Calculate the numerical value of

n_{D}

, giving your answer correct to two decimal places. (iii) A ray of light in air is incident on medium D after passing through the intermediate media as described. Using the value obtained in part (ii), find the ratio of the speed of light in air to that in medium D. (iv) Verify that the relation

n_{DA}\,n_{AD}=1

holds for the pair of media A and D, showing all steps clearly.

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