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प्रश्न
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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उत्तर १
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
उत्तर २
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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