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A thin glass lens of refractive index 1.5 has a focal length of 12 cm in air. When it is completely immersed in a transparent liquid, its focal length increases to 24 cm . If the refractive index of the liquid is x 5 , the value of x is _____.

Correct answer

6

Step-by-step solution

Let the Lens Maker's formula for air be: 1 f_a = ( _g - 1) ( 1 R₁ - 1 R₂ ) For the liquid: 1 f_l = ( _g _l - 1 ) ( 1 R₁ - 1 R₂ ) Dividing the two equations: f_l f_a = _g - 1 _g _l - 1 Substituting the given values ( f_a = 12 cm , f_l = 24 cm , _g = 1.5 ): 24 12 = 1.5 - 1 1.5 _l - 1 2 = 0.5 1.5 _l - 1 1.5 _l - 1 = 0.25 1.5 _l = 1.25 _l = 1.5 1.25 = 6 5 Given that _l = x 5 , we get x = 6 . Answer: 6

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