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Chapter 5: Q17E (page 1152)

34.17 A speck of dirt is embedded 3.50 cm below the surface of a sheet of ice (n=1.309). What is its apparent depth when viewed at normal incidence?

Short Answer

Expert verified

The apparent depth when viewed at normal incidence is 2.67 cm

Step by step solution

01

Formula for Spherical refracting surface with plane surface between two optical materials

nas+nbs'=0

02

Determine the apparent depth of dirt

There is a special case for the spherical refracting surface which is the plane surface between two materials where R=∞. In this case, use the below equation for a plane refracting surface in the form

nas+nbs'=0

where nais the refractive index of ice and equals 1.309, nbis the refractive index of air and equals 1.0. The distance is the distance from the air to the dirt and equals 3.5 cm.s' is the apparent depth. So, solve equation fors'

s'=-(nbna)s

Put the values in above equation,

s'=-(nbna)s=-(1.01.309)3.5cm=-2.67cm

Hence, the apparent depth of dirt is 2.67cm.

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