Question

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

Answer 1

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. 

Answer 2

Answer:

hope it helps you friend