# 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

1
by shireenprince

2015-04-15T21:25:32+05:30

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F_air = + 30 cm

Let 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.