The diameter of the sixth dark Newtonian ring turned out to be D6 = 8.4mm. The installation for obtaining Newton’s

The diameter of the sixth dark Newtonian ring turned out to be D6 = 8.4mm. The installation for obtaining Newton’s rings is illuminated with light lambda = 0.589 µm. Newton’s rings are observed in reflected light. Determine the lens crisis radius R.

This problem can be solved using the formula: r = √ (k * λ * R), where r is the radius of Newton’s dark ring, k is the number of the ring, λ is the length of the light wave, R is the radius of curvature.

r is found as half the diameter of Newton’s ring: r = D ^ 6/2 = 8.4 / 2 = 4.2 mm.

Next, we translate our values from the SI system:

r = 4.2 * 10 ^ – 3 m;

λ = 0.589 * 10 ^ – 6 m;

From the first formula we express R: R = r ^ 2 / k / λ.

Substitute the values: R = (4.2 * 10 ^ – 3) 2/6 / 0.589 * 10 ^ – 6 =

= 4.2 * 4.2 * 10 ^ – 6/6 / 0.589 * 10 ^ – 6 = 17.64 / 3.534 = 4.99 m.

Answer: 4.99 m.