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Question

Figure 9.37 shows an equiconvex lens [of reflective index 1.50] in contact with a liquid layer on top of a plane mirror. A small needle with its up on the principle axis is moved along the axis unit its inverted image is found at the position of the needle.The distance of the needle from the lens is measured to be 45.0cm The liquid is removed and the experiments is repeated. The new distance is measured to be 30.0cm. What is the reflexive index of the liquid?
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Solution

Let focal length of convex lens (glass) ,f1=30cm

focal length of plane concave lens (liquid) isf2

and it is given that combined focal length , F=45cm

we know,

1f1+1f2=1F [ combined focal length formula]

so, 1f2=1F1f1

1f2=145130

f2=(23)90=190

f2=90cm

for lens (glass),

R1=Rand R2=R

use lens maker formula,

1f1=(u1)[1R11R2]

130=(321)[1R+1R]

130=12×2/R=1R

R=30cm

now, for plane concave lens (liquid)

R1=R=30cm , R2=

so, 1f2=(u1)[1R11R2]

190=(u1)[1301]

190=(u1)30

13=u1

u=43

hence, refractive index of liquid is 43


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