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A double convex lens of focal length 30cm is made of glass.When immersed in a liquid of refractive index 1.5 ,the focal length is found to be 120cm. The critical angle between glass and liquids is |
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Answer» + 30 cmLet the refractive index of glass μ_g Liquid of refractive index μ_l = 1.5 when in air, the focal length of the DOUBLE convex lens is GIVEN by : the lens MAKER's formula: 1 / f_air = 1/30 = (μ_g - 1) 2 / R , R = radius of curvature of the lens surface 1/30 *= (μ_g - 1) 2 / R μ_g - 1 = R / 60 --- (1)when immersed in the liquid : 1/f2 = 1/120 = (μ_g / μ_l - 1) 2 / R (μ_g /1.5 - 1) = R /240 -- (2) μ_g - 1.5 = R / 160 -- (3) subtract (2) from (1), 0.5 = R/60 - R /160 = R /96 R = 48 cm μ_g = 1 + 48/60 = 1.8 as per (1) μ_g / μ_l = 1.8/1.5 = 1.2 critical angle between glass and the liquid : Sin⁻¹ 1/1.2 = Sin⁻¹ 0.833 = 56.44 deg. |
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