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Chapter 35: Q77P (page 1077)

A Newton鈥檚 rings apparatus is to be used to determine the radius of curvature of a lens . The radii of the nth and (n+20th)bright rings are found to be 0.162cm and 0.368cm, respectively, in light of wavelength 546nm. Calculate the radius of curvature of the lower surface of the lens.

Short Answer

Expert verified

The radius of the curvature of the lower surface of the lens is 1.0m.

Step by step solution

01

Given data

The radii ofnth=0.162cm

The radii of n+20=0.368cm

Wavelength 位=546nm

02

Definition of newton’s ring

Newton's ring is a phenomenon in which an interference pattern is created by the reflection of light between two surfaces; a spherical surface and an adjacent touching flat surface.

03

Determine the radius of the curvature 

The radius of curvature of the xth ring

Rx=0.162cm

For n+20thRn+20=0.368cm

Let the radius of the curvature of the lower surface of the lens be R.

The value of R is given by as

R=Rn+202-Rx220脳位R=0.368脳10-2鈥�m2-0.162脳10-2鈥�m220脳546脳10-9鈥�mR=0.9998mR=1.0m

Hence, the radius of the curvature of the lower surface of the lens is 1.0m.

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