Question

a liquid of
refractive index en; is poured onto the
concave surface of concave-convex
lens. R1
and R2
are the radii of
curvature of convex and concave
surfaces of the lens respectively and
R1= 2R2
• The refractive index of
material or-lens is n1
. For which
combination of'n1 and n2
, the whole
system behaves as a diverging lens.

Answer 1

Options:   (a) n1 = 1.2,  n2 = 1.8         (b) n1= 1.63,   n2= 1.35
                (c) n1 = 1.56    n2 = 1.38       (d) n1 = 1.7   n2 = 1.33

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We apply the formula for refraction at a spherical surface.  As one side of  the lens we have liquid and on the other side we have  air.

Formula:   n2 / v1  -  n1/u = (n2 - n1) / R

We have a planar surface first (surface of liquid) between air and liquid.

so   n2 / v1 - 1/u = (n2 -1)/∞ = 0

At the surface of radius R2:

      n1 / v2  - n2/ v1  = (n1 - n2) / R2

At the surface of radius R1:

     1 / v  - n1 / v2 =   (1 - n1) / R1

Add the three equations:

    1/v  - 1/u  = (n1 - n2) / R2  - (n1 - 1) / R1

If  n1 < n2 ,  then  RHS is negative.  So focal length will be negative.
Then it will be the diverging lens.   Calculate the  RHS for different options given.

Answer:  from the options in the question,  it should be (a).

Answer 2

as per the question asked option 4 will be correct answer