For a thin convex lens in air, a graph is plotted between 1 v (on y-axis) and 1 u (on x-axis), where u and v are object and image distances respectively. The graph is a straight line which intersects the 1 u axis at the point (-0.05 cm ⁻¹, 0) . The refractive index of the material of the lens is 1.5 . If this lens is completely immersed in a transparent liquid of refractive index 1.25 , its new focal length will be _

Step-by-step solution

The intercept on the 1 u axis occurs when 1 v = 0 . Given the intercept is at -0.05 cm ⁻¹ , we have 1 u = -0.05 cm ⁻¹ when 1 v = 0 . Using the lens formula to find the focal length in air ( f_a ): 1 f_a = 1 v - 1 u = 0 - (-0.05) = 0.05 cm ⁻¹ f_a = 20 cm Using the Lens Maker's formula in air: 1 f_a = ( _g - 1) ( 1 R₁ - 1 R₂ ) 1 20 = (1.5 - 1) ( 1 R₁ - 1 R₂ ) ( 1 R₁ - 1 R₂ ) = 1 10 cm ⁻¹ When the lens is immersed in the liquid, the new focal length ( f_l ) is given by: 1 f_l = ( _g _l - 1 ) ( 1 R₁ - 1 R₂ ) Substitute