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Chapter 34: Q 72 (page 993)

A point source of light is distance d from the surface of a 6.0-cm-diameter glass sphere. For what value of d is there an image at the same distance d on the opposite side of the sphere?

Short Answer

Expert verified

d is equal to 6.0 cm.

Step by step solution

01

Step 1. Given information is :Diameter of spherical glass lens, D = 6.0 cmIndex of refraction of glass, n = 1.50Distance between point source and lens, s = dDistance between image of the point source and lens, s' = d

We need to find out the value of d.

02

Step 2. Applying Lens Maker Formula.

1f=n-11R1-1R2

As the lens is having two equal curved surfaces,

R1=RandR2=-RR=D2

Putting values,

1f=n-11R-1-R1f=n-12R1f=1.50-12R1f=0.502R=1Rf=R

We know that,

1s+1s'=1RPuttingvalues,1d+1d=1R=1D22d=2Dd=Dd=6.0cm

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