Light of a single wavelength, ? = 628 nm, shines down on a planoconvex lens lyin

Question

Light of a single wavelength, ? = 628 nm, shines down on a planoconvex lens lying on a piece of perfectly flat glass, as shown in the figure. When viewed from above, you can see a set of concentric dark and bright fringes, referred to as Newton's rings.

(a) If the radius of the tenth dark ring is 1.70 cm, what is the air gap distance between the lens and the flat glass?

(b) What is the radius of curvature, R, of the lens? (To solve this you will have to use the information found in (a) and look at the geometry of the situation.)

Light of a single wavelength, ? = 628 nm, shines down on a planoconvex lens lying on a piece of perfectly flat glass, as shown in the figure. When viewed from above, you can see a set of concentric dark and bright fringes, referred to as Newton's rings. (a) If the radius of the tenth dark ring is 1.70 cm, what is the air gap distance between the lens and the flat glass? (b) What is the radius of curvature, R, of the lens? (To solve this you will have to use the information found in (a) and look at the geometry of the situation.)

Explanation / Answer

In Newton's ring experiment:
if r is radius of ring and R is radius of curvature
For dark ring
r*r/R = nL (L = wavelength of light)
Here, r = 0.017m
L= 628 nm, n = 10
R= r*r/nL = 46.01m

if t = thickness, for dark fringe
2t = nL
or t = nL/2 = 3.14 * 10-6 m

Answers
a) 3.14 * 10-6 m
b) 46.01m

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