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The glass rod of Exercise 34.25 is immersed in a liquid. An object 14.0 cm from the vertex of the left end of the rod and on its axis is imaged at a point 9.00 cm from the vertex inside the liquid. What is the index of refraction of the liquid?

Short Answer

Expert verified

The refractive index of the liquid is 1.244

Step by step solution

01

 Image-Object relation

Object-Image relationship for spherical reflecting surfaces:

n1s+n2s=n2-n1R

n1,n2=>The refraction index of both the surfaces,s'=> the image distance from the vertex of the spherical surfaces,role="math" localid="1663915194689" s=> the object distance from the vertex of the spherical surface,R=> and the radius of the spherical surface.

n1=required=>liquidn2=1.6(glass)

s = 14cm

s'=-9cm

R is negative because it is in the opposite direction of refracted light

R = - 4cm

02

Calculation

n1s+n1s'=n2-n1R=n2Rn1Rn1s+n1R=n2R-n2s''n11s+1R=n2R-n2s'n1=n2s-n2s'/1s+1R=1.6-4cm-1.6-9cm/114cm+1-4cm=1.244

Hence, the refractive index of the liquid is 1.244

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