Chapter 35: Q77P (page 1077)

A Newton’s rings apparatus is to be used to determine the radius of curvature of a lens . The radii of the nth and $(n + 20 th)$ bright rings are found to be $0.162 cm$ and $0.368 cm$ , respectively, in light of wavelength $546 n m$ . 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 $1.0 m$ .

Step by step solution

Given data

The radii of $n t h = 0.162 cm$

The radii of $(n + 20) = 0.368 cm$

Wavelength $λ = 546 nm$

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.

Determine the radius of the curvature

The radius of curvature of the xth ring

$R_{x} = 0.162 cm$

For ${(n + 20)}^{t h} R_{n + 20} = 0.368 cm$

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

The value of R is given by as

$\begin{array}{rcl} R & = & \frac{R_{n + 20}^{2} - R_{x}^{2}}{20 \times λ} \\ R & = & \frac{{(0.368 \times 10^{- 2} m)}^{2} - {(0.162 \times 10^{- 2} m)}^{2}}{20 \times 546 \times 10^{- 9} m} \\ R & = & 0.9998 m \\ R & = & 1.0 m \end{array}$

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

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Short Answer

Step by step solution

Given data

Definition of newton’s ring

Determine the radius of the curvature

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A Newton’s 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

Step by step solution

Given data

Definition of newton’s ring

Determine the radius of the curvature

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Space Physics

Magnetism

Circular Motion and Gravitation

Electrostatics

Scientific Method Physics

Quantum Physics

Study anywhere. Anytime. Across all devices.