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Question
The optical path of a ray of light of a given wavelength travelling a distance of 3 cm in flint glass having refractive index 1.6 is the same as that on travelling a distance x cm through a medium having a refractive index 1.25. Determine the value of x.
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Solution 1
Let dfg and dm m be the distances by the ray of light in the flint glass and the medium respectively. Also, let nfg and nm be the refractive indices of the flint glass and the medium respectively.
Data: dfg = 3 cm, nfg = 1.6, nm = 1.25,
Optical path = `"n"_"m" xx "d"_"m" = "n"_"fg" xx "d"_"fg"`
∴ `"d"_"m" = ("n"_"fg" xx "d"_"fg")/"n"_"m" = (1.6 xx 3)/1.25 = 3.84` cm
Thus, x cm = 3.84 cm
∴ x = 3.84
Solution 2
Given:
d1 = 3 cm, n1 = 1.6, n2 = 1.25
To find: Optical path in medium 2 (d2)
Formula: n1d1 = n2d2
Calculation:
From formula,
1.6 × 3 = 1.25 × d2
∴ d2 = `(1.6 xx 3)/1.25` = 3.84 cm
The value of x is 3.84 cm.
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