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**Hint:**We have all done this in our childhood taking a magnifying glass/lens and showing our face from it, by doing this we observed that our face looks bigger than usual. This is the play of light passing through the glass/lens and getting refracted. The light is vertically shifted due to the variation in the refractive index (medium). The light goes from a rarer medium (air) to a denser medium (glass).

**Formula Used:**

The relation between thickness of the material, refractive index of the glass and the height of the image formed is given as:

$\delta = t\left( {\mu - 1} \right)$;

Where

$\delta $= Height of the image formed;

$\mu $= refractive index of the glass;

t = Thickness of the material

**Complete step by step answer:**

The shift (vertically) due to variation in refractive index is given by:

$\delta = t\left( {\mu - 1} \right)$;

So, we have 2 objects, write the above equation in terms of the two objects:

${\delta _1} = t\left( {{\mu _1} - 1} \right)$; …(1)

${\delta _2} = t\left( {{\mu _2} - 1} \right)$; …(2)

Find the refractive index of the second glass object${\mu _2}$:

Divide the 1

^{st}equation with the 2

^{nd}equation and solve:

\[\dfrac{{{\delta _1}}}{{{\delta _2}}} = \dfrac{{t\left( {{\mu _1} - 1} \right)}}{{t\left( {{\mu _2} - 1} \right)}}\] ;

\[ \Rightarrow \dfrac{{{\delta _1}}}{{{\delta _2}}} = \dfrac{{\left( {{\mu _1} - 1} \right)}}{{\left( {{\mu _2} - 1} \right)}}\]

Put in the given values in the above equation:

\[\dfrac{{1.5}}{4} = \dfrac{{\left( {\dfrac{3}{2} - 1} \right)}}{{\left( {{\mu _2} - 1} \right)}}\];

\[ \Rightarrow \dfrac{{1.5}}{4} \times \left( {{\mu _2} - 1} \right) = \left( {\dfrac{3}{2} - 1} \right)\];

Simplify the above equation:

\[ \Rightarrow \dfrac{{1.5}}{4} \times \left( {{\mu _2} - 1} \right) = \left( {\dfrac{{3 - 2}}{2}} \right)\];

\[ \Rightarrow \dfrac{{1.5}}{2} \times \left( {{\mu _2} - 1} \right) = 1\];

Solve,

\[ \Rightarrow \left( {{\mu _2} - 1} \right) = \dfrac{2}{{1.5}}\];

\[ \Rightarrow {\mu _2} = \dfrac{2}{{1.5}} + 1\];

The refractive index of the second glass object is:

\[ \Rightarrow {\mu _2} \simeq 2.25\];

**$\therefore$ The correct option is B**

**Note:**Here we have to establish a relation between the height, thickness and the refractive index of the medium, for two glass objects of the same thickness ‘t’. After that divide the first relation with the second relation and find out the refractive index for the second medium.

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