Question

In a Newton's rings experiment the diameter of the 15th ring was found to be 0.590 cm and that of the 5th ring was 0.336 cm. If the radius of the plano-convex lens is 100cm, calculate the wavelength of light used.​

Answer 1

Given info : In a Newton's rings experiment the diameter of the 15th ring was found to be 0.590 cm and that of the 5th ring was 0.336 cm. If the radius of the plano-convex lens is 100cm.

To find : the wavelength of light used.

Solution : using formula, $\lambda=\frac{D_{n+m}^2-D_n^2}{4mR}$

Here diameter of 15th ring, $D_{n+m}$ = 0.59 cm = 5.9 × 10¯³ m

diameter of 5th ring, $D_n$ = 0.336 cm = 3.36 × 10¯³ m

Here, m = 15 - 5 = 10

R = 100 cm = 1 m

So, wavelength, λ = [(5.9 × 10¯³)² - (3.36 × 10¯³)²]/4 × 10 × 1

= {(34.81 - 11.2896)/40} × 10¯⁶

= 23.5204/40 × 10¯⁶

= 0.5880 × 10¯⁶ m

= 5880 A°

Therefore the wavelength of light used is 5880 A°

Answer 2

Explanation:

Solution : using formula, \lambda=\frac{D_{n+m}^2-D_n^2}{4mR}λ=

4mR

D

n+m

2

−D

n

2

Here diameter of 15th ring, D_{n+m}D

n+m

= 0.59 cm = 5.9 × 10¯³ m

diameter of 5th ring, D_nD

n

= 0.336 cm = 3.36 × 10¯³ m

Here, m = 15 - 5 = 10

R = 100 cm = 1 m

So, wavelength, λ = [(5.9 × 10¯³)² - (3.36 × 10¯³)²]/4 × 10 × 1

= {(34.81 - 11.2896)/40} × 10¯⁶

= 23.5204/40 × 10¯⁶

= 0.5880 × 10¯⁶ m

= 5880 A°